Question

$f^{-1}([-\infty,r))$ measurable for all rational numbers $r$

score 629 · Answer 1 · 2026-03-22 14:15:49

629

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$f^{-1}([-\infty,r))$ measurable for all rational numbers $r$

Published on 22 Mar 2026 - 14:15

score 47 · Answer 2 · 2018-04-17 19:17:47

47

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Measure Theory Conjecture: Continuity Preserving Measure of Special Sets

Published on 17 Apr 2018 - 19:17

score 3.6k · Answer 3 · 2018-04-19 11:35:45

3.6k

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Image of Borel set under continuous and injective map

Published on 19 Apr 2018 - 11:35

score 103 · Answer 4 · 2026-03-20 02:54:20

103

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Does Haar measure have such property?

Published on 20 Mar 2026 - 2:54

score 1k · Answer 5 · 2018-04-22 23:27:47

1k

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Chapter 1 Durrett: Show that $R^d$, Borel sets is countably generated.

Published on 22 Apr 2018 - 23:27

score 291 · Answer 6 · 2026-03-22 05:09:35

291

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Not Borel measurable set

Published on 22 Mar 2026 - 5:09

score 186 · Answer 7 · 2026-03-22 08:58:06

186

Views

Closed Set - Closed Set = $F_{\sigma}$ set?

Published on 22 Mar 2026 - 8:58

score 655 · Answer 8 · 2018-05-09 12:34:15

655

Views

Can we obtain the Borel $\sigma$-algebra on $[0;1]$ as a limit of finite algebra?

Published on 09 May 2018 - 12:34

score 177 · Answer 9 · 2026-03-22 04:31:50

177

Views

A set with Borel preimage

Published on 22 Mar 2026 - 4:31

score 581 · Answer 10 · 2026-03-20 02:12:14

581

Views

Is the sum (difference) of Borel set with itself a Borel set?

Published on 20 Mar 2026 - 2:12

score 390 · Answer 11 · 2018-05-16 09:03:55

390

Views

$f:\mathbb R\longrightarrow \mathbb R$ is measurable $\iff$ $f^{-1}(B)$ is measurable for all Borel set $B$

Published on 16 May 2018 - 9:03

score 225 · Answer 12 · 2018-05-16 12:11:14

225

Views

Question on a proof of Kuratowski's Theorem in Kechris's Classical Descriptive Set Theory

Published on 16 May 2018 - 12:11

score 84 · Answer 13 · 2018-05-17 15:30:56

84

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If $f$ is continuous on $A,$ is it true that $\{x:\text{osc}_f(x)=0\}=A?$

Published on 17 May 2018 - 15:30

score 228 · Answer 14 · 2018-05-19 06:24:08

228

Views

Show that for $\xi>1,$ $A \text{ is } \Delta_{\xi+1}^0 \iff A=\lim_nA_n\text{ for some } A_n\in\Delta_\xi^0.$

Published on 19 May 2018 - 6:24

score 279 · Answer 15 · 2026-03-17 06:32:18

279

Views

Projection of a measurable cylinder of the product $\sigma$-algebra

Published on 17 Mar 2026 - 6:32

List Question

$f^{-1}([-\infty,r))$ measurable for all rational numbers $r$

Measure Theory Conjecture: Continuity Preserving Measure of Special Sets

Image of Borel set under continuous and injective map

Does Haar measure have such property?

Chapter 1 Durrett: Show that $R^d$, Borel sets is countably generated.

Not Borel measurable set

Closed Set - Closed Set = $F_{\sigma}$ set?

Can we obtain the Borel $\sigma$-algebra on $[0;1]$ as a limit of finite algebra?

A set with Borel preimage

Is the sum (difference) of Borel set with itself a Borel set?

$f:\mathbb R\longrightarrow \mathbb R$ is measurable $\iff$ $f^{-1}(B)$ is measurable for all Borel set $B$

Question on a proof of Kuratowski's Theorem in Kechris's Classical Descriptive Set Theory

If $f$ is continuous on $A,$ is it true that $\{x:\text{osc}_f(x)=0\}=A?$

Show that for $\xi>1,$ $A \text{ is } \Delta_{\xi+1}^0 \iff A=\lim_nA_n\text{ for some } A_n\in\Delta_\xi^0.$

Projection of a measurable cylinder of the product $\sigma$-algebra

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