Question

If a set is measurable then its image set is measurable.

score 55 · Answer 1 · 2026-04-15 19:42:44

55

Views

If a set is measurable then its image set is measurable.

Published on 15 Apr 2026 - 19:42

score 156 · Answer 2 · 2026-04-14 11:58:12

156

Views

Family of Measurable Sets Implies Measurable Function

Published on 14 Apr 2026 - 11:58

score 214 · Answer 3 · 2026-04-26 16:08:54

214

Views

Monotone Class Theorem for Bounded Nonnegative Functions

Published on 26 Apr 2026 - 16:08

score 211 · Answer 4 · 2026-05-10 15:42:29

211

Views

Right Continuous Adapted Processes without right-continuous Filtration.

Published on 10 May 2026 - 15:42

score 152 · Answer 5 · 2026-04-11 23:42:50

152

Views

Non-increasing Function of Measurable Sets

Published on 11 Apr 2026 - 23:42

score 1k · Answer 6 · 2026-04-14 15:15:28

1k

Views

The inverse of a Borel set

Published on 14 Apr 2026 - 15:15

score 265 · Answer 7 · 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 60 · Answer 8 · 2026-04-16 11:29:47

60

Views

Show that $d_{f+g}(\alpha+\beta) \leq d_{f}(\alpha)+d_{g}(\beta)$, where $d_h(c)=\mu(\{x \in X:|h(x)|>c\}$

Published on 16 Apr 2026 - 11:29

score 551 · Answer 9 · 2026-04-17 15:37:02

551

Views

If for each rational $q$ the set $f^ {−1} ((q,\infty])$ is measurable then $f$ is measurable.

Published on 17 Apr 2026 - 15:37

score 39 · Answer 10 · 2026-05-10 16:33:49

39

Views

Proving a mapping T from d-dimensional R to d-dimensional R is Borel measurable.

Published on 10 May 2026 - 16:33

score 211 · Answer 11 · 2026-05-10 12:55:34

211

Views

Integral in probability space

Published on 10 May 2026 - 12:55

score 150 · Answer 12 · 2026-05-10 16:29:33

150

Views

Show that a function is a Borel function

Published on 10 May 2026 - 16:29

score 181 · Answer 13 · 2026-04-16 15:07:28

181

Views

Prove that $\mathscr{B}(\mathbb{R}^d)$ is a subset of $\mathscr{F}$, a $\sigma$-field

Published on 16 Apr 2026 - 15:07

score 69 · Answer 14 · 2026-04-15 22:47:04

69

Views

Is $\{ x \in [0,1] : \textrm{the sequence }f_1(x),f_2(x),f_3(x),\ldots\textrm{converges}\}$ is measurable?

Published on 15 Apr 2026 - 22:47

score 49 · Answer 15 · 2026-04-12 04:52:57

49

Views

is there any measurable set which is not open,close or Borel?

Published on 12 Apr 2026 - 4:52

List Question

If a set is measurable then its image set is measurable.

Family of Measurable Sets Implies Measurable Function

Monotone Class Theorem for Bounded Nonnegative Functions

Right Continuous Adapted Processes without right-continuous Filtration.

Non-increasing Function of Measurable Sets

The inverse of a Borel set

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 $r$.

Show that $d_{f+g}(\alpha+\beta) \leq d_{f}(\alpha)+d_{g}(\beta)$, where $d_h(c)=\mu(\{x \in X:|h(x)|>c\}$

If for each rational $q$ the set $f^ {−1} ((q,\infty])$ is measurable then $f$ is measurable.

Proving a mapping T from d-dimensional R to d-dimensional R is Borel measurable.

Integral in probability space

Show that a function is a Borel function

Prove that $\mathscr{B}(\mathbb{R}^d)$ is a subset of $\mathscr{F}$, a $\sigma$-field

Is $\{ x \in [0,1] : \textrm{the sequence }f_1(x),f_2(x),f_3(x),\ldots\textrm{converges}\}$ is measurable?

is there any measurable set which is not open,close or Borel?

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