List questions from lebesgue-integral

Published on 15 Apr 2026 - 18:24

331

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Non constructive proof that positive measurable functions can be approximated by a sequence of simple functions?

Published on 11 May 2026 - 8:27

1.1k

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Problem in equality in Chebyshev inequality

Published on 11 Apr 2026 - 8:04

55

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Uniformly $L^2$

Published on 29 Apr 2026 - 11:52

233

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Dominated convergence theorem for absolutely continuous function

Published on 11 Apr 2026 - 17:31

99

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Dominated convergence theorem for absolutely continuous functions 2

Published on 12 Apr 2026 - 21:06

713

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Prove that $\lim_{n \rightarrow \infty} \int_{\Omega} |f_n - f|^{p} dm=0$.

Published on 16 Apr 2026 - 22:03

146

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One step in the proof that the series of $1/{n^2}$ equals ${\pi^2}/6$ that I don't understand

Published on 14 Apr 2026 - 2:03

46

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Measure given by an integral

Published on 09 Apr 2026 - 3:51

225

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Is the gradient somehow 'hidden' behind Lebesgue differentiation theorem?

Published on 12 Apr 2026 - 3:25

388

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Let $f:[a,b]] \to \mathbb{R}$ absolutely continuous and increasing function. Prove $\int_A f'd\lambda=\lambda(f(A))$

Published on 15 Apr 2026 - 11:48

1.2k

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What happens if we try to define the Lebesgue integral by an infimum?

Published on 11 Apr 2026 - 8:13

490

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Show that a function is Lebesgue integrable

Published on 14 Apr 2026 - 1:50

660

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Doing an integral (solution of heat equation)

Published on 09 Apr 2026 - 0:14

128

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Prove that $\lim_{n\to \infty} \int_A f_n d\mu = \int_A fd\mu$

Published on 14 Apr 2026 - 19:40

List Question

$\lim_{y\downarrow 0} yE(1/X ; X>y)=0$

Non constructive proof that positive measurable functions can be approximated by a sequence of simple functions?

Problem in equality in Chebyshev inequality

Uniformly $L^2$

Dominated convergence theorem for absolutely continuous function

Dominated convergence theorem for absolutely continuous functions 2

Prove that $\lim_{n \rightarrow \infty} \int_{\Omega} |f_n - f|^{p} dm=0$.

One step in the proof that the series of $1/{n^2}$ equals ${\pi^2}/6$ that I don't understand

Measure given by an integral

Is the gradient somehow 'hidden' behind Lebesgue differentiation theorem?

Let $f:[a,b]] \to \mathbb{R}$ absolutely continuous and increasing function. Prove $\int_A f'd\lambda=\lambda(f(A))$

What happens if we try to define the Lebesgue integral by an infimum?

Show that a function is Lebesgue integrable

Doing an integral (solution of heat equation)

Prove that $\lim_{n\to \infty} \int_A f_n d\mu = \int_A fd\mu$

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