Question

If for a.e. $x \in X$ the sequence $(f_n(x, \cdot))_n$ is Cauchy in $L^0 (Y)$, then $(f_n)$ is Cauchy in $L^0 (Z)$

score 23 · Answer 1 · 2023-08-23 18:10:07

23

Views

If for a.e. $x \in X$ the sequence $(f_n(x, \cdot))_n$ is Cauchy in $L^0 (Y)$, then $(f_n)$ is Cauchy in $L^0 (Z)$

Published on 23 Aug 2023 - 18:10

score 32 · Answer 2 · 2023-08-23 18:38:43

32

Views

If $f \in L^0 (X, L^0 (Y))$, then $f \in L^0 (Z)$

Published on 23 Aug 2023 - 18:38

score 44 · Answer 3 · 2026-03-29 08:44:42

44

Views

Does Amann's Theorem 1.4 about $\mu$-measurability extend to metrizable topological groups?

Published on 29 Mar 2026 - 8:44

score 55 · Answer 4 · 2026-03-29 14:25:20

55

Views

Topology of convergence in measure is not compatible with the vector space structure of measurable functions

Published on 29 Mar 2026 - 14:25

score 65 · Answer 5 · 2026-03-25 12:53:18

65

Views

Counterexample to Egorov for functions valued in non-separable metric space

Published on 25 Mar 2026 - 12:53

score 295 · Answer 6 · 2026-03-25 14:25:53

295

Views

On the definition of locally integrable functions on an abstract measure space.

Published on 25 Mar 2026 - 14:25

score 50 · Answer 7 · 2023-08-30 01:13:28

50

Views

A Criterion that helps verify if a function $f:\Pi _{i=1}^nX_i\to Y$ is measurable

Published on 30 Aug 2023 - 1:13

score 44 · Answer 8 · 2023-09-11 04:56:52

44

Views

$f_n \to f$ almost uniform if and only if $\lim_{n \to \infty} \mu ( \cup_{m \geq n} |f_m(x) - f_n(x)| \geq \epsilon ) = 0 $

Published on 11 Sep 2023 - 4:56

score 79 · Answer 9 · 2023-09-15 07:50:04

79

Views

Different definitions of the canonical form of simple functions (issue with constant reals different from $0$)

Published on 15 Sep 2023 - 7:50

score 23 · Answer 10 · 2026-03-27 10:48:31

23

Views

Joint measurability of discrete integral.

Published on 27 Mar 2026 - 10:48

score 20 · Answer 11 · 2023-09-21 04:45:45

20

Views

The upper limit of a continuous function on two variables is measurable

Published on 21 Sep 2023 - 4:45

score 62 · Answer 12 · 2023-09-27 17:42:40

62

Views

Uniform Convergence for Functions $X \to [0,+\infty]$?

Published on 27 Sep 2023 - 17:42

score 31 · Answer 13 · 2023-09-27 18:59:15

31

Views

How can I show that if $Y$ is $\mathcal{F}$ measurable then $X$ is also?

Published on 27 Sep 2023 - 18:59

score 108 · Answer 14 · 2023-09-30 03:41:13

108

Views

$\lim_{n\to\infty}\int_X f_n d\mu=2023$ and measures

Published on 30 Sep 2023 - 3:41

score 48 · Answer 15 · 2023-09-30 19:10:57

48

Views

Prove that a continuous and $\mathcal{F}_t$ adapted process is progressively measurable

Published on 30 Sep 2023 - 19:10

List Question

If for a.e. $x \in X$ the sequence $(f_n(x, \cdot))_n$ is Cauchy in $L^0 (Y)$, then $(f_n)$ is Cauchy in $L^0 (Z)$

If $f \in L^0 (X, L^0 (Y))$, then $f \in L^0 (Z)$

Does Amann's Theorem 1.4 about $\mu$-measurability extend to metrizable topological groups?

Topology of convergence in measure is not compatible with the vector space structure of measurable functions

Counterexample to Egorov for functions valued in non-separable metric space

On the definition of locally integrable functions on an abstract measure space.

A Criterion that helps verify if a function $f:\Pi _{i=1}^nX_i\to Y$ is measurable

$f_n \to f$ almost uniform if and only if $\lim_{n \to \infty} \mu ( \cup_{m \geq n} |f_m(x) - f_n(x)| \geq \epsilon ) = 0 $

Different definitions of the canonical form of simple functions (issue with constant reals different from $0$)

Joint measurability of discrete integral.

The upper limit of a continuous function on two variables is measurable

Uniform Convergence for Functions $X \to [0,+\infty]$?

How can I show that if $Y$ is $\mathcal{F}$ measurable then $X$ is also?

$\lim_{n\to\infty}\int_X f_n d\mu=2023$ and measures

Prove that a continuous and $\mathcal{F}_t$ adapted process is progressively measurable

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