Question

For a Borel subset $B$ of a complete, seperable metric space $S$ and $\epsilon > 0$, there exists compact $C \subset S$ with $P(B) < P(C) + \epsilon$.

score 19 · Answer 1 · 2024-03-19 13:34:07

19

Views

For a Borel subset $B$ of a complete, seperable metric space $S$ and $\epsilon > 0$, there exists compact $C \subset S$ with $P(B) < P(C) + \epsilon$.

Published on 19 Mar 2024 - 13:34

score 24 · Answer 2 · 2026-02-23 23:09:20

24

Views

Limit of the measure of the delta neighborhood of Borel Sets.

Published on 23 Feb 2026 - 23:09

score 1.4k · Answer 3 · 2017-05-01 15:20:30

1.4k

Views

Proof that the discrete probability measures are dense in the space of all Borel probability

Published on 01 May 2017 - 15:20

score 161 · Answer 4 · 2017-10-19 21:12:14

161

Views

Regularity of a finite borel measure on the compact subsets of $\mathbb{R^d}$

Published on 19 Oct 2017 - 21:12

score 73 · Answer 5 · 2017-10-20 18:17:34

73

Views

$\int_X f_n d\mu_1 \to \int_X fd\mu_1 $ and $\int_X f_n d\mu_2\to \int_X f d\mu_2$ for a bounded Borel function $f$

Published on 20 Oct 2017 - 18:17

score 1.6k · Answer 6 · 2017-10-27 15:19:00

1.6k

Views

Show that $f:\mathbb{R}\to\mathbb{R}$ is Borel measurable if $f$ is either right continuous or left continuous.

Published on 27 Oct 2017 - 15:19

score 727 · Answer 7 · 2017-10-29 11:26:04

727

Views

Show that the set of all real numbers whose decimal notation includes the number 2 are borel measurable

Published on 29 Oct 2017 - 11:26

score 668 · Answer 8 · 2017-10-30 03:36:09

668

Views

How many Borel sigma algebra are there on the real number set?

Published on 30 Oct 2017 - 3:36

score 73 · Answer 9 · 2017-10-31 03:26:03

73

Views

$A_n\downarrow A \implies \mu(A_n) \downarrow \mu(A)$ need not be true when $\mu(A_1) = \infty$

Published on 31 Oct 2017 - 3:26

score 630 · Answer 10 · 2017-11-01 19:25:19

630

Views

If $E$ is a Borel measurable set, show that there exists a subset of $E$ with half measure.

Published on 01 Nov 2017 - 19:25

score 54 · Answer 11 · 2017-11-02 23:22:40

54

Views

Finding a non-measurable function

Published on 02 Nov 2017 - 23:22

score 33 · Answer 12 · 2017-11-06 13:37:20

33

Views

Measurability of f, defining the right intervals.

Published on 06 Nov 2017 - 13:37

score 593 · Answer 13 · 2017-11-12 21:19:43

593

Views

Lebesgue Outer Measure is not Finitely Additive.

Published on 12 Nov 2017 - 21:19

score 376 · Answer 14 · 2017-11-15 19:19:14

376

Views

Borel $\sigma$-algebra generated by pseudo base

Published on 15 Nov 2017 - 19:19

score 336 · Answer 15 · 2017-11-19 05:28:30

336

Views

Translation is continuous in $L^1$ for finite Borel measures

Published on 19 Nov 2017 - 5:28

List Question

For a Borel subset $B$ of a complete, seperable metric space $S$ and $\epsilon > 0$, there exists compact $C \subset S$ with $P(B) < P(C) + \epsilon$.

Limit of the measure of the delta neighborhood of Borel Sets.

Proof that the discrete probability measures are dense in the space of all Borel probability

Regularity of a finite borel measure on the compact subsets of $\mathbb{R^d}$

$\int_X f_n d\mu_1 \to \int_X fd\mu_1 $ and $\int_X f_n d\mu_2\to \int_X f d\mu_2$ for a bounded Borel function $f$

Show that $f:\mathbb{R}\to\mathbb{R}$ is Borel measurable if $f$ is either right continuous or left continuous.

Show that the set of all real numbers whose decimal notation includes the number 2 are borel measurable

How many Borel sigma algebra are there on the real number set?

$A_n\downarrow A \implies \mu(A_n) \downarrow \mu(A)$ need not be true when $\mu(A_1) = \infty$

If $E$ is a Borel measurable set, show that there exists a subset of $E$ with half measure.

Finding a non-measurable function

Measurability of f, defining the right intervals.

Lebesgue Outer Measure is not Finitely Additive.

Borel $\sigma$-algebra generated by pseudo base

Translation is continuous in $L^1$ for finite Borel measures

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