Question

Question on Borel Set $X = \Bbb{Q} \times (\Bbb{R} \setminus \Bbb{Q})$

score 122 · Answer 1 · 2019-11-05 11:23:56

122

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Question on Borel Set $X = \Bbb{Q} \times (\Bbb{R} \setminus \Bbb{Q})$

Published on 05 Nov 2019 - 11:23

score 67 · Answer 2 · 2019-11-06 11:12:10

67

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Proof of contrapositive of Lemma 1.5.3 of book Measure Theory, by Donald L. Cohn

Published on 06 Nov 2019 - 11:12

score 96 · Answer 3 · 2019-11-06 20:58:14

96

Views

Is there a non-random variable with Borel set preimage?

Published on 06 Nov 2019 - 20:58

score 333 · Answer 4 · 2019-11-08 14:07:41

333

Views

$\inf$ and $\sup$ of two real random variables

Published on 08 Nov 2019 - 14:07

score 96 · Answer 5 · 2019-11-11 09:26:03

96

Views

$(\Omega,\mathscr{F},\mu):=((-1,1),\mathscr{B}((-1,1)),\lambda)$ is $f(x,y):=\dfrac{xy}{(x^2+y^2)^2}$measurable?

Published on 11 Nov 2019 - 9:26

score 164 · Answer 6 · 2026-03-25 12:51:06

164

Views

Computing product measure.

Published on 25 Mar 2026 - 12:51

score 272 · Answer 7 · 2026-03-25 10:58:19

272

Views

The Lebesgue measure satisfies $\lambda(x+E)=\lambda(E)$

Published on 25 Mar 2026 - 10:58

score 316 · Answer 8 · 2026-03-25 19:10:41

316

Views

Measurability of distance function

Published on 25 Mar 2026 - 19:10

score 141 · Answer 9 · 2026-03-07 10:54:42

141

Views

Example for a non-Borel set $A$ in $\mathbb{R}^2$ such that all $x$- and $y$- sections are measurable

Published on 07 Mar 2026 - 10:54

score 193 · Answer 10 · 2026-03-25 12:12:15

193

Views

Measurable function with parameters

Published on 25 Mar 2026 - 12:12

score 83 · Answer 11 · 2019-11-22 04:12:51

83

Views

Proving that the set of continuous real functions is dense in the norm $L_{1}$ in the set of integrable functions

Published on 22 Nov 2019 - 4:12

score 37 · Answer 12 · 2019-11-23 20:01:45

37

Views

Representation of Borel functions

Published on 23 Nov 2019 - 20:01

score 86 · Answer 13 · 2026-03-25 10:52:44

86

Views

Is every measurable function in a Borel sigma algebra defined only on open sets?

Published on 25 Mar 2026 - 10:52

score 123 · Answer 14 · 2019-12-03 17:19:27

123

Views

Formal article to read that the Borel $\sigma$-algebra is properly contained in the Lebesgue $\sigma$-algebra?

Published on 03 Dec 2019 - 17:19

score 63 · Answer 15 · 2019-12-03 22:45:40

63

Views

Show that the set of points $x$ where $(f_{n}(x))$ is convergent is a Borel subset of $\mathbb{R}$

Published on 03 Dec 2019 - 22:45

List Question

Question on Borel Set $X = \Bbb{Q} \times (\Bbb{R} \setminus \Bbb{Q})$

Proof of contrapositive of Lemma 1.5.3 of book Measure Theory, by Donald L. Cohn

Is there a non-random variable with Borel set preimage?

$\inf$ and $\sup$ of two real random variables

$(\Omega,\mathscr{F},\mu):=((-1,1),\mathscr{B}((-1,1)),\lambda)$ is $f(x,y):=\dfrac{xy}{(x^2+y^2)^2}$measurable?

Computing product measure.

The Lebesgue measure satisfies $\lambda(x+E)=\lambda(E)$

Measurability of distance function

Example for a non-Borel set $A$ in $\mathbb{R}^2$ such that all $x$- and $y$- sections are measurable

Measurable function with parameters

Proving that the set of continuous real functions is dense in the norm $L_{1}$ in the set of integrable functions

Representation of Borel functions

Is every measurable function in a Borel sigma algebra defined only on open sets?

Formal article to read that the Borel $\sigma$-algebra is properly contained in the Lebesgue $\sigma$-algebra?

Show that the set of points $x$ where $(f_{n}(x))$ is convergent is a Borel subset of $\mathbb{R}$

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