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 222 · Answer 1 · 2026-04-14 19:48:18

222

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 14 Apr 2026 - 19:48

score 33 · Answer 2 · 2026-04-15 07:13:56

33

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 15 Apr 2026 - 7:13

score 196 · Answer 3 · 2026-04-30 14:40:19

196

Views

Length of intervals

Published on 30 Apr 2026 - 14:40

score 99 · Answer 4 · 2026-04-12 10:53:26

99

Views

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

Published on 12 Apr 2026 - 10:53

score 271 · Answer 5 · 2026-04-14 06:26:31

271

Views

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

Published on 14 Apr 2026 - 6:26

score 327 · Answer 6 · 2026-04-13 02:28:56

327

Views

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

Published on 13 Apr 2026 - 2:28

score 499 · Answer 7 · 2026-04-14 11:17:19

499

Views

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

Published on 14 Apr 2026 - 11:17

score 148 · Answer 8 · 2026-05-10 14:40:35

148

Views

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

Published on 10 May 2026 - 14:40

score 84 · Answer 9 · 2026-05-10 14:40:35

84

Views

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

Published on 10 May 2026 - 14:40

score 55 · Answer 10 · 2026-04-13 18:41:19

55

Views

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

Published on 13 Apr 2026 - 18:41

score 647 · Answer 11 · 2026-04-13 22:03:37

647

Views

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

Published on 13 Apr 2026 - 22:03

score 980 · Answer 12 · 2026-04-13 01:33:07

980

Views

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

Published on 13 Apr 2026 - 1:33

score 612 · Answer 13 · 2026-05-10 15:18:03

612

Views

Is the set of measurable functions measurable?

Published on 10 May 2026 - 15:18

score 393 · Answer 14 · 2026-04-09 05:38:55

393

Views

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

Published on 09 Apr 2026 - 5:38

score 81 · Answer 15 · 2026-04-16 10:40:12

81

Views

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

Published on 16 Apr 2026 - 10:40

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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