Question

Can a Cartesian product of nonelements of Sigma Algebras be in the Product Sigma Algebra?

score 459 · Answer 1 · 2026-04-10 20:36:23

459

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Can a Cartesian product of nonelements of Sigma Algebras be in the Product Sigma Algebra?

Published on 10 Apr 2026 - 20:36

score 425 · Answer 2 · 2026-04-15 09:55:17

425

Views

A sequence of measurable function and a set points such that this sequence converge

Published on 15 Apr 2026 - 9:55

score 276 · Answer 3 · 2026-04-16 05:40:28

276

Views

understanding $\int_{F} E[X|\mathcal{F}]dP=\int_F E[X]dP$ in the definition of conditional expectation

Published on 16 Apr 2026 - 5:40

score 60 · Answer 4 · 2026-04-17 01:03:52

60

Views

If $(f_{n})_{n}$ are measurable prove $A := \{x : \lim f_{n}(x)\text{ exists}\}$ is measurable

Published on 17 Apr 2026 - 1:03

score 263 · Answer 5 · 2026-04-13 14:51:23

263

Views

Is the integral of a continuous map always a Radon measure?

Published on 13 Apr 2026 - 14:51

score 296 · Answer 6 · 2026-04-15 15:20:49

296

Views

Dirac measure as an image of pushforward map

Published on 15 Apr 2026 - 15:20

score 498 · Answer 7 · 2026-04-12 13:07:25

498

Views

Using monotone convergence to prove that the limit of a measure of increasing sets is the measure of the union

Published on 12 Apr 2026 - 13:07

score 432 · Answer 8 · 2026-04-16 17:56:33

432

Views

Is there a set $E$ such that for every open interval $I$, $0<m(I\cap E)<m(I)$?

Published on 16 Apr 2026 - 17:56

score 365 · Answer 9 · 2026-04-29 12:41:14

365

Views

Continuity implies $\mu$-strongly measurability?

Published on 29 Apr 2026 - 12:41

score 4.1k · Answer 10 · 2026-04-13 06:18:30

4.1k

Views

Every measurable function is the limit a.e of a sequence of continuous functions

Published on 13 Apr 2026 - 6:18

score 121 · Answer 11 · 2026-04-16 11:51:20

Suppose $A_i$ is an increasing sequence of sets from a sigma algebra. Is $sup\{\mu(A_i)\} = \mu\bigg(\bigcup\limits_{i=1}^{\infty} A_i\bigg)$?

score 379 · Answer 12 · 2026-04-17 03:32:15

379

Views

$\{µ(E) : E ∈ S\} = [0, 1] ∪ [3, c]$. Prove that $c ≥ 4$. Can you give an example of $(X, S, µ)$ if $c = 4$?

Published on 17 Apr 2026 - 3:32

score 276 · Answer 13 · 2026-04-25 18:27:28

276

Views

$\mathbb{Q}$ is not a $G_{\delta}$ What is wrong with my argument?

Published on 25 Apr 2026 - 18:27

score 265 · Answer 14 · 2026-04-15 05:25:23

265

Views

Suppose $(X, \mathcal{A})$ is a measurable space, $f$ is a real-valued function, and $\{x:f(x)>r\} \in\mathcal{A}$ for each rational number $r$.

Published on 15 Apr 2026 - 5:25

score 389 · Answer 15 · 2026-04-11 18:13:51

389

Views

Lebesgue integral of function zero

Published on 11 Apr 2026 - 18:13

List Question

Can a Cartesian product of nonelements of Sigma Algebras be in the Product Sigma Algebra?

A sequence of measurable function and a set points such that this sequence converge

understanding $\int_{F} E[X|\mathcal{F}]dP=\int_F E[X]dP$ in the definition of conditional expectation

If $(f_{n})_{n}$ are measurable prove $A := \{x : \lim f_{n}(x)\text{ exists}\}$ is measurable

Is the integral of a continuous map always a Radon measure?

Dirac measure as an image of pushforward map

Using monotone convergence to prove that the limit of a measure of increasing sets is the measure of the union

Is there a set $E$ such that for every open interval $I$, $0<m(I\cap E)<m(I)$?

Continuity implies $\mu$-strongly measurability?

Every measurable function is the limit a.e of a sequence of continuous functions

Suppose $A_i$ is an increasing sequence of sets from a sigma algebra. Is $sup\{\mu(A_i)\} = \mu\bigg(\bigcup\limits_{i=1}^{\infty} A_i\bigg)$?

$\{µ(E) : E ∈ S\} = [0, 1] ∪ [3, c]$. Prove that $c ≥ 4$. Can you give an example of $(X, S, µ)$ if $c = 4$?

$\mathbb{Q}$ is not a $G_{\delta}$ What is wrong with my argument?

Suppose $(X, \mathcal{A})$ is a measurable space, $f$ is a real-valued function, and $\{x:f(x)>r\} \in\mathcal{A}$ for each rational number $r$.

Lebesgue integral of function zero

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