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Bharath KrishnanIn a magazine article [1] on problems and progress in quantum field theory, Wood writes of Feynman path integrals, “No known mathematical procedure can meaningfully average an infinite number of objects covering an infinite expanse of space in general. The path integral is more of a physics philosophy than an exact mathematical recipe.”This article [2] provides a method for averaging an arbitrary collection of objects; however, the average can be any number in the extension of the range of these objects. (Note, an arbitrary collection of these objects is a function.)Question: Suppose anything meaningful has applications in quantum field theory. Is there a way to meaningfully choose a unique, finite average of a function whose graph matches the description in Wood's quote?For more info, see this post [3].[1]: <a href="https://www.quantamagazine.org/mathematicians-prove-2d-version-of-quantum-gravity-really-works-20210617/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.quantamagazine.org/mathematicians-prove-2d-version-of-quantum-gravity-really-works-20210617/</a>[2]: <a href="https://arxiv.org/pdf/2004.09103" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/pdf/2004.09103</a>[3]: <a href="https://math.stackexchange.com/q/5052005/125918" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://math.stackexchange.com/q/5052005/125918</a><a href="https://mathstodon.xyz/tags/PathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PathIntegral</a> <a href="https://mathstodon.xyz/tags/quantum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quantum</a> <a href="https://mathstodon.xyz/tags/FeynmanPathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FeynmanPathIntegral</a> <a href="https://mathstodon.xyz/tags/mean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mean</a> <a href="https://mathstodon.xyz/tags/average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#average</a> <a href="https://mathstodon.xyz/tags/expectedvalue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#expectedvalue</a> <a href="https://mathstodon.xyz/tags/quantumfieldtheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quantumfieldtheory</a>

WIST Quotations<a href="https://wist.info/mclaughlin-mignon/75961/" rel="nofollow noopener noreferrer" target="_blank">A quotation from Mignon McLaughlin</a><blockquote>Your children are neither as bad nor as good as you imagine. But then, neither are you.</blockquote>Mignon McLaughlin (1913-1983) American journalist and author The Neurotic’s Notebook, ch. 2 (1963) Sourcing, notes: <a href="https://wist.info/mclaughlin-mignon/75961/" rel="nofollow noopener noreferrer" target="_blank">wist.info/mclaughlin-mignon/75…</a><a href="https://my-place.social/search?tag=quote" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quote</a> <a href="https://my-place.social/search?tag=quotes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quotes</a> <a href="https://my-place.social/search?tag=quotation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quotation</a> <a href="https://my-place.social/search?tag=qotd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#qotd</a> <a href="https://my-place.social/search?tag=character" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#character</a> <a href="https://my-place.social/search?tag=assessment" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#assessment</a> <a href="https://my-place.social/search?tag=average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#average</a> <a href="https://my-place.social/search?tag=badbehavior" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#badbehavior</a> <a href="https://my-place.social/search?tag=children" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#children</a> <a href="https://my-place.social/search?tag=goodbehavior" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#goodbehavior</a> <a href="https://my-place.social/search?tag=parenting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#parenting</a> <a href="https://my-place.social/search?tag=quality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quality</a> <a href="https://my-place.social/search?tag=selfassessment" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#selfassessment</a> <a href="https://my-place.social/search?tag=selfawareness" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#selfawareness</a> <a href="https://my-place.social/search?tag=subjectivity" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#subjectivity</a>

CpaphilVINTAGE POSTCARD Football Works of the plays of the soldier Average Football<a href="https://www.cpaphil.com/en/products/pages/2?search=football" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.cpaphil.com/en/products/pages/2?search=football</a><a href="https://mastodon.social/tags/Football" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Football</a> <a href="https://mastodon.social/tags/Works" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Works</a> <a href="https://mastodon.social/tags/Plays" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Plays</a> <a href="https://mastodon.social/tags/Soldier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Soldier</a> <a href="https://mastodon.social/tags/Average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Average</a> <a href="https://mastodon.social/tags/VintagePostcard" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#VintagePostcard</a> <a href="https://mastodon.social/tags/History" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#History</a> <a href="https://mastodon.social/tags/Heritage" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Heritage</a> <a href="https://mastodon.social/tags/VintageArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#VintageArt</a> <a href="https://mastodon.social/tags/Memory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Memory</a> <a href="https://mastodon.social/tags/Illustration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Illustration</a> <a href="https://mastodon.social/tags/HistoricalPostcard" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HistoricalPostcard</a> <a href="https://mastodon.social/tags/FootballArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FootballArt</a> <a href="https://mastodon.social/tags/ArtisticDesign" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ArtisticDesign</a>

Kevin Karhan :verified:<a href="https://mastodon.online/@setebos" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@setebos</a> you even crimped it properly and made it comply with <a href="https://infosec.space/tags/VDE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#VDE</a> standards...<ul><li>This is <a href="https://www.youtube.com/watch?v=MsgR7uUxyhQ" rel="nofollow noopener noreferrer" target="_blank">beyond</a> <a href="https://infosec.space/tags/Averag%C3%A9" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Averagé</a> by a long shot!</li></ul>

Bharath KrishnanI finally know what I want. Let \(n\in\mathbb{N}\) and suppose function \(f:A\subseteq\mathbb{R}^{n}\to\mathbb{R}\), where \(A\) and \(f\) are Borel. Let \(\text{dim}_{\text{H}}(\cdot)\) be the Hausdorff dimension, where \(\mathcal{H}^{\text{dim}_{\text{H}}(\cdot)}(\cdot)\) is the Hausdorff measure in its dimension on the Borel \(\sigma\)-algebra.§1. MotivationSuppose, we define everywhere surjective \(f\):Let \((A,\mathrm{T})\) be a standard topology. A function \(f:A\subseteq\mathbb{R}^{n}\to\mathbb{R}\) is everywhere surjective from \(A\) to \(\mathbb{R}\), if \(f[V]=\mathbb{R}\) for every \(V\in\mathrm{T}\).If f is everywhere surjective, whose graph has zero Hausdorff measure in its dimension (e.g., [1]), we want a unique, satisfying [2] average of \(f\), taking finite values only. However, the expected value of \(f\):\[\mathbb{E}[f]=\frac{1}{{\mathcal{H}}^{\text{dim}_{\text{H}}(A)}(A)}\int_{A}f\, d{\mathcal{H}}^{\text{dim}_{\text{H}}(A)}\]is undefined since the integral of \(f\) is undefined: i.e., the graph of \(f\) has Hausdorff dimension \(n+1\) with zero \((n+1)\)-dimensional Hausdorff measure. Thus, w.r.t a reference point \(C\in\mathbb{R}^{n+1}\), choose any sequence of bounded functions converging to \(f\) [2, §2.1] with the same satisfying [2, §4] and finite expected value [2, §2.2].[1]: <a href="https://mathoverflow.net/questions/476471/is-there-an-explicit-everywhere-surjective-f-mathbbr-to-mathbbr-whose-gr" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://mathoverflow.net/questions/476471/is-there-an-explicit-everywhere-surjective-f-mathbbr-to-mathbbr-whose-gr</a>[2]: <a href="https://www.researchgate.net/publication/389499633_Defining_a_Unique_Satisfying_Expected_Value_From_Chosen_Sequences_of_Bounded_Functions_Converging_to_an_Everywhere_Surjective_Function/stats" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.researchgate.net/publication/389499633_Defining_a_Unique_Satisfying_Expected_Value_From_Chosen_Sequences_of_Bounded_Functions_Converging_to_an_Everywhere_Surjective_Function/stats</a><a href="https://mathstodon.xyz/tags/HausdorffMeasure" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HausdorffMeasure</a> <a href="https://mathstodon.xyz/tags/HausdorffDimension" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HausdorffDimension</a> <a href="https://mathstodon.xyz/tags/EverywhereSurjectiveFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EverywhereSurjectiveFunction</a> <a href="https://mathstodon.xyz/tags/ExpectedValue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExpectedValue</a> <a href="https://mathstodon.xyz/tags/Average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Average</a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#research</a>

Kevin Karhan :verified:<a href="https://chaosfem.tw/@JoscelynTransient" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@JoscelynTransient</a> I'd not do that literally.<ul><li>You know how many <a href="https://infosec.space/tags/drugs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#drugs</a> the <a href="https://infosec.space/tags/average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#average</a> <a href="https://infosec.space/tags/billionaire" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#billionaire</a> has in their system?</li></ul>Pretty shure <a href="https://infosec.space/tags/Musk" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Musk</a> himself has more <a href="https://infosec.space/tags/Ketamine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Ketamine</a> in himself than most vets dish out on a busy Monday...

WIST Quotations<a href="https://wist.info/taleb-nassim-nicholas/75320/" rel="nofollow noopener noreferrer" target="_blank">A quotation from Nassim Taleb</a><blockquote>Mild success can be explainable by skills and labor. Wild success is attributable to variance.</blockquote>Nassim Nicholas Taleb (b. 1960) Lebanese-American essayist, statistician, risk analyst, aphorist. Fooled by Randomness, Part 1, ch. 1 (2001) Sourcing, notes: <a href="https://wist.info/taleb-nassim-nicholas/75320/" rel="nofollow noopener noreferrer" target="_blank">wist.info/taleb-nassim-nichola…</a><a href="https://my-place.social/search?tag=quote" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quote</a> <a href="https://my-place.social/search?tag=quotes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quotes</a> <a href="https://my-place.social/search?tag=quotation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quotation</a> <a href="https://my-place.social/search?tag=odds" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#odds</a> <a href="https://my-place.social/search?tag=chance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#chance</a> <a href="https://my-place.social/search?tag=average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#average</a> <a href="https://my-place.social/search?tag=goodluck" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#goodluck</a> <a href="https://my-place.social/search?tag=hardwork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#hardwork</a> <a href="https://my-place.social/search?tag=labor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#labor</a> <a href="https://my-place.social/search?tag=luck" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#luck</a> <a href="https://my-place.social/search?tag=skill" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#skill</a> <a href="https://my-place.social/search?tag=success" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#success</a> <a href="https://my-place.social/search?tag=variance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#variance</a>

gentlegardenerImportant interview with <a href="https://mastodon.scot/tags/privileged" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#privileged</a> <a href="https://mastodon.scot/tags/treasurysec" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#treasurysec</a> <a href="https://mastodon.scot/tags/bessent" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bessent</a> on <a href="https://mastodon.scot/tags/BloombergTV" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BloombergTV</a> <a href="https://mastodon.scot/tags/federalworkforce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#federalworkforce</a> <a href="https://mastodon.scot/tags/dogees" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dogees</a> <a href="https://mastodon.scot/tags/tusk" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tusk</a> <a href="https://mastodon.scot/tags/ukraine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ukraine</a> <a href="https://mastodon.scot/tags/zelensky" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#zelensky</a> <a href="https://mastodon.scot/tags/Protip" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Protip</a> <a href="https://mastodon.scot/tags/media" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#media</a> interviews: Never call anyone an “ <a href="https://mastodon.scot/tags/averageAmerican" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#averageAmerican</a>”. Nor their kids <a href="https://mastodon.scot/tags/average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#average</a>. You have no experience of life outside your bubble of <a href="https://mastodon.scot/tags/privilege" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#privilege</a>. Working for the gummint was steady work with steady benefits. Your idea is to make everyone grovel.And learn to stop smirking on camera. Save it for <a href="https://mastodon.scot/tags/SiliconValley" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SiliconValley</a> <a href="https://flipboard.com/@bloomberg" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@bloomberg</a>

Nando161<a href="https://partyon.xyz/tags/Average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Average</a> <a href="https://partyon.xyz/tags/Western" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Western</a> "<a href="https://partyon.xyz/tags/journalist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#journalist</a>".

-0--1-<a href="https://ohai.social/@MennoWolff" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@MennoWolff</a> <a href="https://cyberplace.social/@iam_sysop" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@iam_sysop</a> The <a href="https://mastodon.social/tags/Median" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Median</a> and <a href="https://mastodon.social/tags/Average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Average</a> <a href="https://mastodon.social/tags/Wealth" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Wealth</a> of <a href="https://mastodon.social/tags/Billionaires" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Billionaires</a> will vary significantly.

Gladwyn d’Souza<a href="https://sfba.social/tags/AbolishThePrisons" class="mention hashtag" rel="tag">#AbolishThePrisons</a>: Roy Wood Jr. after busting though dead dogs, double parked broom sticks, doors on doors, and the frantic search for content says starting at 7:44 excuse me but the <a href="https://sfba.social/tags/MediaCircus" class="mention hashtag" rel="tag">#MediaCircus</a> over the <a href="https://sfba.social/tags/arraignment" class="mention hashtag" rel="tag">#arraignment</a> was oblivious to the show put on by the <a href="https://sfba.social/tags/IndictedInsurector" class="mention hashtag" rel="tag">#IndictedInsurector</a> that obfuscated him not getting the full <a href="https://sfba.social/tags/CriminalJustice" class="mention hashtag" rel="tag">#CriminalJustice</a> treatment meant to <a href="https://sfba.social/tags/dehumanize" class="mention hashtag" rel="tag">#dehumanize</a> the <a href="https://sfba.social/tags/average" class="mention hashtag" rel="tag">#average</a> person. <a href="https://youtu.be/TBRGdhSF3WA" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://youtu.be/TBRGdhSF3WA</a>

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