List questions from measure-theory

Published on 09 Apr 2026 - 20:50

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A function that is continuous almost everywhere is Lebesgue measurable

Published on 12 Apr 2026 - 14:06

53

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Given rectangle $L \subseteq \mathbb{R}^n$ st. $v(L) = r$, can we cover $L$ by countably many rectangles $Q_i$ s.t. $\sum_{i=1}^{\infty}v(Q_i) < r$?

Published on 16 Apr 2026 - 14:50

41

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Transfering order to conditional expectation

Published on 31 Mar 2026 - 10:28

338

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An unpleasant measure theory/functional analysis problem

Published on 08 Apr 2026 - 17:00

82

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If $f(x,u(x))$ measuable with conditions

Published on 11 May 2026 - 1:16

57

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Write $[0,1]^\mathbb{N}$ as a disjoint union of two measurable subsets such that non of which contain a cylinder.

Published on 16 Apr 2026 - 4:04

63

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Struggling to understand step in proof regarding a sequence of measurable functions

Published on 10 Apr 2026 - 22:09

350

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if $\{x| f(x) \neq g(x))\}$ has zero measure then $\int f = \int g$.

Published on 16 Apr 2026 - 18:27

96

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Almost sure and order convergence are equivalent in $L_p$ spaces

Published on 14 May 2026 - 8:36

305

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Lebesgue-Radon-Nikodym decomposition

Published on 09 Apr 2026 - 9:30

134

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Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

Published on 10 May 2026 - 16:35

244

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Almost complete convergence

Published on 12 Apr 2026 - 6:50

774

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Radon-Nikodym derivative of a limit of measures with bounded R.-N. derivative

Published on 09 Apr 2026 - 11:22

33

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Sequence of functions who are bounded from below, change of limit and integral

Published on 13 Apr 2026 - 1:33

List Question

Fourier transformation of bump functions

A function that is continuous almost everywhere is Lebesgue measurable

Given rectangle $L \subseteq \mathbb{R}^n$ st. $v(L) = r$, can we cover $L$ by countably many rectangles $Q_i$ s.t. $\sum_{i=1}^{\infty}v(Q_i) < r$?

Transfering order to conditional expectation

An unpleasant measure theory/functional analysis problem

If $f(x,u(x))$ measuable with conditions

Write $[0,1]^\mathbb{N}$ as a disjoint union of two measurable subsets such that non of which contain a cylinder.

Struggling to understand step in proof regarding a sequence of measurable functions

if $\{x| f(x) \neq g(x))\}$ has zero measure then $\int f = \int g$.

Almost sure and order convergence are equivalent in $L_p$ spaces

Lebesgue-Radon-Nikodym decomposition

Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

Almost complete convergence

Radon-Nikodym derivative of a limit of measures with bounded R.-N. derivative

Sequence of functions who are bounded from below, change of limit and integral

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