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#lebesgue

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Jocelyn<p><span class="h-card" translate="no"><a href="https://mamot.fr/@Gallorum" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>Gallorum</span></a></span> </p><p>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">#<span>Lebesgue</span></a> pour du <a href="https://mastodon.gougere.fr/tags/Reuleaux" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reuleaux</span></a>.</p><p><a href="https://mastodon.gougere.fr/tags/IlikeToRideMyBicycle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>IlikeToRideMyBicycle</span></a> <a href="https://mastodon.gougere.fr/tags/Bike" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Bike</span></a></p><p><a href="https://inv.nadeko.net/watch?v=oobpwxMKD0s" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inv.nadeko.net/watch?v=oobpwxM</span><span class="invisible">KD0s</span></a></p>
Pustam | पुस्तम | পুস্তম🇳🇵<p>DOMINATED CONVERGENCE THEOREM<br>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="nofollow noopener noreferrer" target="_blank">#<span>Lebesgue</span></a> integration more powerful than <a href="https://mathstodon.xyz/tags/Riemann" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Riemann</span></a> integration. The theorem an be stated as follows:</p><p>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</p><p>\[\displaystyle\lim_{n\to\infty}\int_\mathcal{S}f_n\ \mathrm{d}\mu=\int_\mathcal{S}f\ \mathrm{d}\mu\]<br><a href="https://mathstodon.xyz/tags/ConvergenceTheorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ConvergenceTheorem</span></a> <a href="https://mathstodon.xyz/tags/Convergence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Convergence</span></a> <a href="https://mathstodon.xyz/tags/DominatedConvergenceTheorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DominatedConvergenceTheorem</span></a> <a href="https://mathstodon.xyz/tags/Lebesgue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Lebesgue</span></a> <a href="https://mathstodon.xyz/tags/MeasurableFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MeasurableFunction</span></a> <a href="https://mathstodon.xyz/tags/LebesgueFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LebesgueFunction</span></a> <a href="https://mathstodon.xyz/tags/LebesgueIntegration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LebesgueIntegration</span></a> <a href="https://mathstodon.xyz/tags/RiemannIntegration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>RiemannIntegration</span></a> <a href="https://mathstodon.xyz/tags/MeasureSpace" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MeasureSpace</span></a></p>
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