Question

Let $f: \Omega \to [0, \infty]$ be measurable. Let $\mu$ be $\sigma$-finite. Then $\{t\mid \mu\{f = t\} \neq 0 \}$ is countable.

score 219 · Answer 1 · 2018-11-10 17:16:20

219

Views

Let $f: \Omega \to [0, \infty]$ be measurable. Let $\mu$ be $\sigma$-finite. Then $\{t\mid \mu\{f = t\} \neq 0 \}$ is countable.

Published on 10 Nov 2018 - 17:16

score 30 · Answer 2 · 2018-11-11 06:59:45

30

Views

Representation of a $\mathbb Z^d$ valued RV $Y$ as $Y=\sum_{k=1}^n e_{Z_k}$ where $Z_1\le Z_2\le...\le Z_n$

Published on 11 Nov 2018 - 6:59

score 192 · Answer 3 · 2018-11-12 01:05:10

192

Views

Length of intervals

Published on 12 Nov 2018 - 1:05

score 96 · Answer 4 · 2018-11-13 01:39:33

96

Views

Can you prove Lusin's theorem without using approximation of $L_1$ functions?

Published on 13 Nov 2018 - 1:39

score 268 · Answer 5 · 2018-11-16 22:11:07

268

Views

If $Z$ is $\sigma(X,Y)$-measurable, is there a measurable $f$ with $Z=f(X,Y)$?

Published on 16 Nov 2018 - 22:11

score 324 · Answer 6 · 2018-11-21 14:48:43

324

Views

Is the domain of convergence of a sequence of measurable functions measurable? (general targets)

Published on 21 Nov 2018 - 14:48

score 496 · Answer 7 · 2018-11-21 15:00:43

496

Views

Let $f$ be non negative and $\int_\Omega fd\mu$ is finite then f is finite valued almost everywhere

Published on 21 Nov 2018 - 15:00

score 145 · Answer 8 · 2026-03-25 01:18:44

145

Views

If $f_n \longrightarrow f$ almost everywhere and $g_n \longrightarrow g$ almost everywhere

Published on 25 Mar 2026 - 1:18

score 81 · Answer 9 · 2026-03-24 23:49:52

81

Views

If either $f_n \longrightarrow f $ almost everywhere OR $f_n \longrightarrow f$

Published on 24 Mar 2026 - 23:49

score 52 · Answer 10 · 2018-11-23 22:01:59

52

Views

Show that $f$ is measurable on $(a,b)$

Published on 23 Nov 2018 - 22:01

score 644 · Answer 11 · 2018-11-27 03:21:40

644

Views

must a measure-preserving and order-preserving bijection have measurable inverse?

Published on 27 Nov 2018 - 3:21

score 977 · Answer 12 · 2018-11-29 05:03:56

977

Views

Convergence in $L^1$ implies there exists a subsequence that converges almost everywhere.

Published on 29 Nov 2018 - 5:03

score 608 · Answer 13 · 2018-11-30 13:42:14

608

Views

Is the set of measurable functions measurable?

Published on 30 Nov 2018 - 13:42

score 390 · Answer 14 · 2018-12-01 21:14:42

390

Views

Showing that a set is Lebesgue Measurable in Higher Dimensions and Applying Fubini's Theorem

Published on 01 Dec 2018 - 21:14

score 78 · Answer 15 · 2018-12-13 13:11:21

78

Views

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

Published on 13 Dec 2018 - 13:11

List Question

Let $f: \Omega \to [0, \infty]$ be measurable. Let $\mu$ be $\sigma$-finite. Then $\{t\mid \mu\{f = t\} \neq 0 \}$ is countable.

Representation of a $\mathbb Z^d$ valued RV $Y$ as $Y=\sum_{k=1}^n e_{Z_k}$ where $Z_1\le Z_2\le...\le Z_n$

Length of intervals

Can you prove Lusin's theorem without using approximation of $L_1$ functions?

If $Z$ is $\sigma(X,Y)$-measurable, is there a measurable $f$ with $Z=f(X,Y)$?

Is the domain of convergence of a sequence of measurable functions measurable? (general targets)

Let $f$ be non negative and $\int_\Omega fd\mu$ is finite then f is finite valued almost everywhere

If $f_n \longrightarrow f$ almost everywhere and $g_n \longrightarrow g$ almost everywhere

If either $f_n \longrightarrow f $ almost everywhere OR $f_n \longrightarrow f$

Show that $f$ is measurable on $(a,b)$

must a measure-preserving and order-preserving bijection have measurable inverse?

Convergence in $L^1$ implies there exists a subsequence that converges almost everywhere.

Is the set of measurable functions measurable?

Showing that a set is Lebesgue Measurable in Higher Dimensions and Applying Fubini's Theorem

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

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