List questions from lebesgue-integral

Published on 25 Feb 2026 - 2:26

37

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Prove that if either $f \in (L^p \cap C^m)(\mathbb{R}^n)$, or $g \in (L^q \cap C^m)(\mathbb{R}^n)$, then $f \ast g \in C^m$

Published on 01 Apr 2026 - 17:07

82

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Show that $\lim_{x\rightarrow0}\frac{e^{\iota x}-1}{\iota x}=1$

Published on 29 Mar 2026 - 8:35

60

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Give a function in $L^p$ but not in weak $L^p$

Published on 11 Apr 2026 - 20:48

44

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The nonnegative set of compact subset of $L^p$ is compact.

Published on 11 Apr 2026 - 19:53

63

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Integral of squared dot product (quadratic form)

Published on 12 Apr 2026 - 4:39

258

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Rudin's RCA - Chapter 9 Exercise 2 - Fourier transform maps $L^1$ to a dense subset of $C_0$

Published on 08 Apr 2026 - 0:46

59

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Total variation of a class in $L^1 [0, 1]$ and lower semicontinuity

Published on 25 Mar 2026 - 23:38

70

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How to use Fubini's theorem to prove the following estimate?

Published on 10 Apr 2026 - 19:03

123

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Continuity of Lebesgue integral

Published on 09 Apr 2026 - 13:23

133

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Convergence in $L^p$ spaces for $0 < p \leq 1$.

Published on 11 Apr 2026 - 11:18

107

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For each $z \in \mathbb{C}$, evaluate $\int_0^1 \int_0^{2\pi} \frac{1}{r e^{i\theta} + z} \, d \theta\, dr.$

Published on 29 Jun 2023 - 4:34

179

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$f$ measurable and bounded over a set of finite measure is integrable

Published on 30 Jun 2023 - 15:40

44

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Show $g(x) = \int_{(0,+\infty)} f(u)e^{-xu} du$ is continuous given that $f$ is integrable

Published on 30 Jun 2023 - 19:10

81

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does the nonstandard grid integral coincide with the lebesgue integral

Published on 10 Apr 2026 - 17:40

List Question

Convergence in sequential Lebesgue spaces.

Prove that if either $f \in (L^p \cap C^m)(\mathbb{R}^n)$, or $g \in (L^q \cap C^m)(\mathbb{R}^n)$, then $f \ast g \in C^m$

Show that $\lim_{x\rightarrow0}\frac{e^{\iota x}-1}{\iota x}=1$

Give a function in $L^p$ but not in weak $L^p$

The nonnegative set of compact subset of $L^p$ is compact.

Integral of squared dot product (quadratic form)

Rudin's RCA - Chapter 9 Exercise 2 - Fourier transform maps $L^1$ to a dense subset of $C_0$

Total variation of a class in $L^1 [0, 1]$ and lower semicontinuity

How to use Fubini's theorem to prove the following estimate?

Continuity of Lebesgue integral

Convergence in $L^p$ spaces for $0 < p \leq 1$.

For each $z \in \mathbb{C}$, evaluate $\int_0^1 \int_0^{2\pi} \frac{1}{r e^{i\theta} + z} \, d \theta\, dr.$

$f$ measurable and bounded over a set of finite measure is integrable

Show $g(x) = \int_{(0,+\infty)} f(u)e^{-xu} du$ is continuous given that $f$ is integrable

does the nonstandard grid integral coincide with the lebesgue integral

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