List questions from lebesgue-integral

Published on 13 Dec 2014 - 10:10

52

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Lebesgue integral of cardinal

Published on 13 Dec 2014 - 17:00

191

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Lebesgue integrable function in rationals

Published on 13 Dec 2014 - 18:07

562

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Find a function in $L^p(\mathbb{R})$ only for $p=4$

Published on 13 Dec 2014 - 22:44

85

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control of an integral using maximal function

Published on 13 Dec 2014 - 22:52

165

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$\lim_{n \to \infty} \int_X f_n \, d\mu = \int_X f \, d\mu$ implies $\lim_{n \to \infty} \int_B f_n \, d\mu = \int_B f \, d\mu$ for $B \subseteq X$

Published on 14 Dec 2014 - 5:05

670

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Measure Spaces: Uniform & Integral Convergence

Published on 01 Apr 2026 - 19:12

400

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Using the MCT to evaluate the integral of a series

Published on 15 Dec 2014 - 4:15

1.9k

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If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

Published on 15 Dec 2014 - 4:19

8.3k

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Inequality between $L^2$- and $L^1$-norms for functions

Published on 25 Mar 2026 - 13:54

544

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If $\int_E f=\int_E g$ then $f=g$ a.e.?

Published on 16 Dec 2014 - 7:01

76

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If $\int_x^z f=0$ for every $z\in[x,y]$, then $f(a)=0$ a.e. on $[x,y]$.

Published on 16 Dec 2014 - 17:31

2.4k

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If $f_n \to f$ and $g_n \to g$ in $L^p$, and $g_n$ is uniformly bounded, then $f_ng_n \to fg$

Published on 17 Dec 2014 - 3:04

314

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An a.e.-defined derivative which is not Lebesgue integrable on any interval?

Published on 01 Apr 2026 - 19:07

107

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Why is $E[X1_A]=0$ if $P(A)=0$?

Published on 18 Dec 2014 - 18:56

List Question

Convergence of series by using counting measure

Lebesgue integral of cardinal

Lebesgue integrable function in rationals

Find a function in $L^p(\mathbb{R})$ only for $p=4$

control of an integral using maximal function

$\lim_{n \to \infty} \int_X f_n \, d\mu = \int_X f \, d\mu$ implies $\lim_{n \to \infty} \int_B f_n \, d\mu = \int_B f \, d\mu$ for $B \subseteq X$

Measure Spaces: Uniform & Integral Convergence

Using the MCT to evaluate the integral of a series

If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

Inequality between $L^2$- and $L^1$-norms for functions

If $\int_E f=\int_E g$ then $f=g$ a.e.?

If $\int_x^z f=0$ for every $z\in[x,y]$, then $f(a)=0$ a.e. on $[x,y]$.

If $f_n \to f$ and $g_n \to g$ in $L^p$, and $g_n$ is uniformly bounded, then $f_ng_n \to fg$

An a.e.-defined derivative which is not Lebesgue integrable on any interval?

Why is $E[X1_A]=0$ if $P(A)=0$?

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