![real analysis - An inequality in the proof of Lebesgue Dominated Convergence Theorem in Royden's book. - Mathematics Stack Exchange real analysis - An inequality in the proof of Lebesgue Dominated Convergence Theorem in Royden's book. - Mathematics Stack Exchange](https://i.stack.imgur.com/JGmPR.jpg)
real analysis - An inequality in the proof of Lebesgue Dominated Convergence Theorem in Royden's book. - Mathematics Stack Exchange
![Sam Walters ☕️ على X: "A simple application of the Lebesgue Dominated Convergence Theorem gives us the Taylor-MacLaurin series for logarithm (which also holds for certain complex numbers). #calculus #math https://t.co/6XsUByqxWJ" / Sam Walters ☕️ على X: "A simple application of the Lebesgue Dominated Convergence Theorem gives us the Taylor-MacLaurin series for logarithm (which also holds for certain complex numbers). #calculus #math https://t.co/6XsUByqxWJ" /](https://pbs.twimg.com/media/EDG_aGgUEAAf6bS.jpg:large)
Sam Walters ☕️ على X: "A simple application of the Lebesgue Dominated Convergence Theorem gives us the Taylor-MacLaurin series for logarithm (which also holds for certain complex numbers). #calculus #math https://t.co/6XsUByqxWJ" /
![SOLVED: Please prove this theorem. Theorem 3.30 (Dominated convergence theorem). Let fi, f2, ... E L(X) satisfy the following assertions: (1) There exists f such that lim fn(x) = f(x) a.e. x e SOLVED: Please prove this theorem. Theorem 3.30 (Dominated convergence theorem). Let fi, f2, ... E L(X) satisfy the following assertions: (1) There exists f such that lim fn(x) = f(x) a.e. x e](https://cdn.numerade.com/ask_images/ce71ae35c8924befa4d27b3a5f9a2458.jpg)
SOLVED: Please prove this theorem. Theorem 3.30 (Dominated convergence theorem). Let fi, f2, ... E L(X) satisfy the following assertions: (1) There exists f such that lim fn(x) = f(x) a.e. x e
![real analysis - Showing that Lebesgue Dominated convergence theorem is false in case of Riemann integration. - Mathematics Stack Exchange real analysis - Showing that Lebesgue Dominated convergence theorem is false in case of Riemann integration. - Mathematics Stack Exchange](https://i.stack.imgur.com/4g2vA.png)
real analysis - Showing that Lebesgue Dominated convergence theorem is false in case of Riemann integration. - Mathematics Stack Exchange
![MathType on X: "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 #Lebesgue MathType on X: "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 #Lebesgue](https://pbs.twimg.com/media/E9zXHWcXMAAFLcd.jpg:large)