Question

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

score 52 · Answer 1 · 2018-08-19 12:59:28

52

Views

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

Published on 19 Aug 2018 - 12:59

score 153 · Answer 2 · 2018-09-02 17:16:54

153

Views

Family of Measurable Sets Implies Measurable Function

Published on 02 Sep 2018 - 17:16

score 208 · Answer 3 · 2026-03-16 23:39:53

208

Views

Monotone Class Theorem for Bounded Nonnegative Functions

Published on 16 Mar 2026 - 23:39

score 207 · Answer 4 · 2018-09-18 01:39:53

207

Views

Right Continuous Adapted Processes without right-continuous Filtration.

Published on 18 Sep 2018 - 1:39

score 149 · Answer 5 · 2018-09-23 17:09:25

149

Views

Non-increasing Function of Measurable Sets

Published on 23 Sep 2018 - 17:09

score 1k · Answer 6 · 2018-09-27 06:19:10

1k

Views

The inverse of a Borel set

Published on 27 Sep 2018 - 6:19

score 262 · Answer 7 · 2018-09-28 13:36:12

262

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 28 Sep 2018 - 13:36

score 57 · Answer 8 · 2018-09-29 17:38:45

57

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 29 Sep 2018 - 17:38

score 548 · Answer 9 · 2018-09-30 22:09:26

548

Views

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

Published on 30 Sep 2018 - 22:09

score 35 · Answer 10 · 2018-10-02 22:21:54

35

Views

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

Published on 02 Oct 2018 - 22:21

score 206 · Answer 11 · 2018-10-02 22:43:32

206

Views

Integral in probability space

Published on 02 Oct 2018 - 22:43

score 146 · Answer 12 · 2018-10-03 18:11:14

146

Views

Show that a function is a Borel function

Published on 03 Oct 2018 - 18:11

score 178 · Answer 13 · 2018-10-09 13:35:03

178

Views

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

Published on 09 Oct 2018 - 13:35

score 66 · Answer 14 · 2018-10-11 20:10:01

66

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 11 Oct 2018 - 20:10

score 46 · Answer 15 · 2018-10-12 15:35:34

46

Views

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

Published on 12 Oct 2018 - 15:35

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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