List questions from measure-theory

Published on 13 Apr 2026 - 2:19

37

Views

For $f\in L^1(\mu)$, $\lim_{t\to \infty}(\mu\{x: |f(x)|>t\})=0$

Published on 19 Apr 2026 - 14:08

83

Views

Asymptotic independence on the tail field is equivalent to a probability measure's being trivial

Published on 25 Mar 2026 - 16:03

89

Views

Definition of the surface measure in some Book

Published on 15 Apr 2026 - 7:54

991

Views

Continuous map from subset of $\mathcal{C}$ (Cantor) to non-measurable set.

Published on 13 May 2026 - 3:37

24

Views

Surjectivity of composition of functions

Published on 09 Apr 2026 - 9:30

120

Views

Uniform measure on an affine variety

Published on 10 May 2026 - 14:06

504

Views

Approximate Borel set by compact set

Published on 14 Apr 2026 - 17:57

56

Views

Show that any nondecreasing $f:[0,\infty)\to\mathbb R$ of locally bounded variation admits a unique signed measure $\mu$ with $\mu([a,b])=f(b)-f(a)$

Published on 10 May 2026 - 13:50

43

Views

Verification of alternative proof of $\lim_{p\to \infty}\|u\|_p=\|u\|_\infty$

Published on 16 Apr 2026 - 0:45

104

Views

Metric space associated with measure space is path-connected

Published on 16 May 2026 - 20:29

412

Views

How to prove that Riemann integrable function is measurable?

Published on 16 May 2026 - 21:16

44

Views

Calculate the value of $\int_0^1 |f'|$

Published on 16 Apr 2026 - 1:25

965

Views

Weak$^*$ convergence in $L^1$

Published on 16 Apr 2026 - 21:26

54

Views

Integral around the mean value of measure

Published on 12 Apr 2026 - 23:37

List Question

Integrability with respect to a spectral measure

For $f\in L^1(\mu)$, $\lim_{t\to \infty}(\mu\{x: |f(x)|>t\})=0$

Asymptotic independence on the tail field is equivalent to a probability measure's being trivial

Definition of the surface measure in some Book

Continuous map from subset of $\mathcal{C}$ (Cantor) to non-measurable set.

Surjectivity of composition of functions

Uniform measure on an affine variety

Approximate Borel set by compact set

Show that any nondecreasing $f:[0,\infty)\to\mathbb R$ of locally bounded variation admits a unique signed measure $\mu$ with $\mu([a,b])=f(b)-f(a)$

Verification of alternative proof of $\lim_{p\to \infty}\|u\|_p=\|u\|_\infty$

Metric space associated with measure space is path-connected

How to prove that Riemann integrable function is measurable?

Calculate the value of $\int_0^1 |f'|$

Weak$^*$ convergence in $L^1$

Integral around the mean value of measure

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