List questions from measure-theory

Published on 14 Apr 2026 - 2:03

74

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$\lim_{n \to \infty}\int_0^1\frac{\sqrt{n^3}\sin x}{1 + n^2 x^2}d\lambda(x) = 0$

Published on 16 Apr 2026 - 23:05

117

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What is the definition of $s$-dimensional Lebesgue measure on $R^d$ for $s\ne d$?

Published on 13 Apr 2026 - 9:54

90

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Proving "uniform convergence" to measurable function

Published on 17 Apr 2026 - 6:21

898

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a.e. pointwise limit of measurable functions

Published on 14 Apr 2026 - 1:07

260

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Lebesgue's Theorem for Riemann Integrability Overkill?

Published on 12 Apr 2026 - 3:34

26

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Does there exist only one such function up to constant?

Published on 13 Apr 2026 - 7:53

126

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Lebesgue integral of non-negative measurable sequence of functions (not monotone)

Published on 11 Apr 2026 - 17:58

120

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Prove $ \ \int_E f(x)dx=\int_E f(x+t)dx \ $

Published on 17 Apr 2026 - 5:23

2.2k

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Vitali's Theorem for Convergence in Measure

Published on 11 Apr 2026 - 20:18

40

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$L^p$ convergence and $L^q$ boundedness implies $L^q$ boundedness.

Published on 16 Apr 2026 - 19:42

170

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What is the definition of "allmost all" in probability theory?

Published on 06 Apr 2026 - 22:57

301

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Size of a Language?

Published on 10 Apr 2026 - 20:29

55

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Finding limit of a convergent sequence

Published on 12 Apr 2026 - 14:29

74

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comparison of the limits of the expectations of two sequences of r.v.

Published on 12 Apr 2026 - 18:06

List Question

How to prove that $ \mathcal{P}(X) \subset \sigma (\mathcal{E})$?

$\lim_{n \to \infty}\int_0^1\frac{\sqrt{n^3}\sin x}{1 + n^2 x^2}d\lambda(x) = 0$

What is the definition of $s$-dimensional Lebesgue measure on $R^d$ for $s\ne d$?

Proving "uniform convergence" to measurable function

a.e. pointwise limit of measurable functions

Lebesgue's Theorem for Riemann Integrability Overkill?

Does there exist only one such function up to constant?

Lebesgue integral of non-negative measurable sequence of functions (not monotone)

Prove $ \ \int_E f(x)dx=\int_E f(x+t)dx \ $

Vitali's Theorem for Convergence in Measure

$L^p$ convergence and $L^q$ boundedness implies $L^q$ boundedness.

What is the definition of "allmost all" in probability theory?

Size of a Language?

Finding limit of a convergent sequence

comparison of the limits of the expectations of two sequences of r.v.

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