Question

Borel $\sigma$-algebra with $\sigma$-finite measure: does a function vanish almost everywhere outside its essential support?

score 46 · Answer 1 · 2026-03-26 08:04:28

46

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Borel $\sigma$-algebra with $\sigma$-finite measure: does a function vanish almost everywhere outside its essential support?

Published on 26 Mar 2026 - 8:04

score 110 · Answer 2 · 2022-08-26 10:58:58

110

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The cardinality of Borel set and real number

Published on 26 Aug 2022 - 10:58

score 72 · Answer 3 · 2026-02-23 12:09:15

72

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Let $\mu$ be a Borel measure and $x_n \to x$. Is it true that $\mu (B(x_n, r)) \to \mu (B(x, r))$?

Published on 23 Feb 2026 - 12:09

score 205 · Answer 4 · 2022-08-28 14:31:23

205

Views

The catch in proving that a singleton is a Borel set?

Published on 28 Aug 2022 - 14:31

score 122 · Answer 5 · 2022-08-29 08:59:19

122

Views

What is the meaning of open intervals in (0, 1]?

Published on 29 Aug 2022 - 8:59

score 81 · Answer 6 · 2022-09-01 20:39:02

81

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Inverse of the function $f(\theta) =\exp(i\theta)$ is Borel measurable

Published on 01 Sep 2022 - 20:39

score 91 · Answer 7 · 2022-09-03 12:35:26

91

Views

In a probability space $(\Omega , \mathcal{F} , P)$, what is the meaning of $P(d w)$

Published on 03 Sep 2022 - 12:35

score 56 · Answer 8 · 2022-09-04 22:43:45

56

Views

Is the set of two measurable functions being equal to each other a measurable set?

Published on 04 Sep 2022 - 22:43

score 64 · Answer 9 · 2022-09-15 18:21:35

64

Views

Is $\mathbb{P}((a,b)) = \tan^{-1}(b) - \tan^{-1}(a)$ a valid probability measure on $X = (0, \infty)$

Published on 15 Sep 2022 - 18:21

score 46 · Answer 10 · 2022-09-17 19:10:03

46

Views

The space of all Borel probability measures is connected w.r.t. the topology induced by weak convergence

Published on 17 Sep 2022 - 19:10

score 65 · Answer 11 · 2022-09-20 13:23:03

65

Views

Show $\sigma (A) = \mathscr{B} (\mathbb{R})$

Published on 20 Sep 2022 - 13:23

score 73 · Answer 12 · 2026-02-24 15:02:04

73

Views

Let $f$ be differentiable s.t. $f'>0$ everywhere and $\nu = f_{\sharp} \mu$. Is $\nu \ll \mu$?

Published on 24 Feb 2026 - 15:02

score 68 · Answer 13 · 2022-10-03 19:10:54

68

Views

Proving a set is a Borel Set

Published on 03 Oct 2022 - 19:10

score 126 · Answer 14 · 2022-10-04 15:36:55

126

Views

Continuous functions measurable => sigma algebra includes Borel algebra

Published on 04 Oct 2022 - 15:36

score 147 · Answer 15 · 2022-10-07 20:55:11

147

Views

Rudin's RCA, Theorem $2.17$.

Published on 07 Oct 2022 - 20:55

List Question

Borel $\sigma$-algebra with $\sigma$-finite measure: does a function vanish almost everywhere outside its essential support?

The cardinality of Borel set and real number

Let $\mu$ be a Borel measure and $x_n \to x$. Is it true that $\mu (B(x_n, r)) \to \mu (B(x, r))$?

The catch in proving that a singleton is a Borel set?

What is the meaning of open intervals in (0, 1]?

Inverse of the function $f(\theta) =\exp(i\theta)$ is Borel measurable

In a probability space $(\Omega , \mathcal{F} , P)$, what is the meaning of $P(d w)$

Is the set of two measurable functions being equal to each other a measurable set?

Is $\mathbb{P}((a,b)) = \tan^{-1}(b) - \tan^{-1}(a)$ a valid probability measure on $X = (0, \infty)$

The space of all Borel probability measures is connected w.r.t. the topology induced by weak convergence

Show $\sigma (A) = \mathscr{B} (\mathbb{R})$

Let $f$ be differentiable s.t. $f'>0$ everywhere and $\nu = f_{\sharp} \mu$. Is $\nu \ll \mu$?

Proving a set is a Borel Set

Continuous functions measurable => sigma algebra includes Borel algebra

Rudin's RCA, Theorem $2.17$.

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