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Jocelyn<a href="https://mamot.fr/@Gallorum" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@Gallorum</a> Alors c'est relou, du coup vaut mieux troquer <a href="https://mastodon.gougere.fr/tags/Lebesgue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lebesgue</a> pour du <a href="https://mastodon.gougere.fr/tags/Reuleaux" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Reuleaux</a>.<a href="https://mastodon.gougere.fr/tags/IlikeToRideMyBicycle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IlikeToRideMyBicycle</a> <a href="https://mastodon.gougere.fr/tags/Bike" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Bike</a><a href="https://inv.nadeko.net/watch?v=oobpwxMKD0s" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://inv.nadeko.net/watch?v=oobpwxMKD0s</a>

Pustam | पुस्तम | পুস্তম🇳🇵DOMINATED CONVERGENCE THEOREM Lebesgue's dominated convergence theorem provides sufficient conditions under which pointwise convergence of a sequence of functions implies convergence of the integrals. It's one of the reasons that makes <a href="https://mathstodon.xyz/tags/Lebesgue" class="mention hashtag" rel="tag">#Lebesgue</a> integration more powerful than <a href="https://mathstodon.xyz/tags/Riemann" class="mention hashtag" rel="tag">#Riemann</a> integration. The theorem an be stated as follows:Let \((f_n)\) be a sequence of measurable functions on a measure space \((\mathcal{S},\Sigma,\mu)\). Suppose that \((f_n)\) converges pointwise to a function \(f\) and is dominated by some Lebesgue integrable function \(g\), i.e. \(|f_n(x)|\leq g(x)\ \forall n\) and \(\forall x\in\mathcal{S}\). Then, \(f\) is Lebesgue integrable, and\[\displaystyle\lim_{n\to\infty}\int_\mathcal{S}f_n\ \mathrm{d}\mu=\int_\mathcal{S}f\ \mathrm{d}\mu\] <a href="https://mathstodon.xyz/tags/ConvergenceTheorem" class="mention hashtag" rel="tag">#ConvergenceTheorem</a> <a href="https://mathstodon.xyz/tags/Convergence" class="mention hashtag" rel="tag">#Convergence</a> <a href="https://mathstodon.xyz/tags/DominatedConvergenceTheorem" class="mention hashtag" rel="tag">#DominatedConvergenceTheorem</a> <a href="https://mathstodon.xyz/tags/Lebesgue" class="mention hashtag" rel="tag">#Lebesgue</a> <a href="https://mathstodon.xyz/tags/MeasurableFunction" class="mention hashtag" rel="tag">#MeasurableFunction</a> <a href="https://mathstodon.xyz/tags/LebesgueFunction" class="mention hashtag" rel="tag">#LebesgueFunction</a> <a href="https://mathstodon.xyz/tags/LebesgueIntegration" class="mention hashtag" rel="tag">#LebesgueIntegration</a> <a href="https://mathstodon.xyz/tags/RiemannIntegration" class="mention hashtag" rel="tag">#RiemannIntegration</a> <a href="https://mathstodon.xyz/tags/MeasureSpace" class="mention hashtag" rel="tag">#MeasureSpace</a>

katch wreck`It is also called the <a href="https://mastodon.social/tags/Cantor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Cantor</a> ternary <a href="https://mastodon.social/tags/function" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#function</a>, the <a href="https://mastodon.social/tags/Lebesgue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lebesgue</a> function, Lebesgue's singular function..the Devil's staircase, the Cantor <a href="https://mastodon.social/tags/staircase" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#staircase</a> function, and the Cantor–Lebesgue function. Georg Cantor (1884) introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental <a href="https://mastodon.social/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> of <a href="https://mastodon.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> claimed by Harnack.`<a href="https://en.wikipedia.org/wiki/Cantor_function" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Cantor_function</a><a href="https://mastodon.social/tags/devilsStaircase" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#devilsStaircase</a> <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a> <a href="https://mastodon.social/tags/cantorSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cantorSet</a> <a href="https://mastodon.social/tags/topology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#topology</a> <a href="https://mastodon.social/tags/analysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#analysis</a>

katch wreck`In <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a>, the Lebesgue differentiation <a href="https://mastodon.social/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> is a theorem of real <a href="https://mastodon.social/tags/analysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#analysis</a>, which states that for almost every point, the value of an <a href="https://mastodon.social/tags/integrable" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#integrable</a> <a href="https://mastodon.social/tags/function" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#function</a> is the limit of <a href="https://mastodon.social/tags/infinitesimal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#infinitesimal</a> averages taken about the point. The theorem is named for Henri <a href="https://mastodon.social/tags/Lebesgue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lebesgue</a>. ` <a href="https://en.wikipedia.org/wiki/Lebesgue_differentiation_theorem" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Lebesgue_differentiation_theorem</a>

Saad<a href="https://mathstodon.xyz/tags/Riemann" class="mention hashtag" rel="tag">#Riemann</a> <a href="https://mathstodon.xyz/tags/Lebesgue" class="mention hashtag" rel="tag">#Lebesgue</a> <a href="https://mathstodon.xyz/tags/integration" class="mention hashtag" rel="tag">#integration</a>

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