Question

Are there inner and outer approximation theorems for arbitrary measures?

score 402 · Answer 1 · 2026-05-10 16:58:18

402

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Are there inner and outer approximation theorems for arbitrary measures?

Published on 10 May 2026 - 16:58

score 58 · Answer 2 · 2026-05-11 09:31:07

58

Views

probability density of a probability density of a probability density ... limiting distribution?

Published on 11 May 2026 - 9:31

score 129 · Answer 3 · 2026-05-10 16:56:53

129

Views

Continuity from below of outer measure extending an algebrea

Published on 10 May 2026 - 16:56

score 120 · Answer 4 · 2026-04-15 22:50:41

120

Views

Convergence of a sequence of measures of sets implies convergence of the indicator functions.

Published on 15 Apr 2026 - 22:50

score 252 · Answer 5 · 2026-04-15 13:50:04

252

Views

The proof of Caratheodory's criterion from Bogachev's book

Published on 15 Apr 2026 - 13:50

score 898 · Answer 6 · 2026-04-14 01:19:56

898

Views

Integral inequality of measurable functions for every measurable set implies function inequality a.e. as long as measure is $\sigma$-finite

Published on 14 Apr 2026 - 1:19

score 1.7k · Answer 7 · 2026-04-15 20:54:51

1.7k

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Show that the market is arbitrage free if $a < S_0^1(1+r)< b$

Published on 15 Apr 2026 - 20:54

score 86 · Answer 8 · 2026-05-10 19:14:34

86

Views

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

Published on 10 May 2026 - 19:14

score 116 · Answer 9 · 2026-05-11 03:13:25

116

Views

Two Baire measure, $\left\{A\subseteq X: A \text{ Baire set}\ \mu(A)=\nu(A)\right\}$ is $\sigma$-algebra

Published on 11 May 2026 - 3:13

score 111 · Answer 10 · 2026-04-12 14:06:11

111

Views

A family of continuous distribution functions with a singular law to the Lebesgue measure

Published on 12 Apr 2026 - 14:06

score 151 · Answer 11 · 2026-05-10 14:06:43

151

Views

Why $\frac{dx}{|x|}$ is a Haar measure on $\mathbb{R}\setminus\{0\}$

Published on 10 May 2026 - 14:06

score 39 · Answer 12 · 2026-04-14 05:01:08

39

Views

Hausdorff measure (open subset containing x)

Published on 14 Apr 2026 - 5:01

score 277 · Answer 13 · 2026-04-11 21:49:06

277

Views

For which measures does the monotone convergence theorem hold?

Published on 11 Apr 2026 - 21:49

score 115 · Answer 14 · 2026-04-11 20:36:45

Finding an increasing sequence of Lebesgue integrable functions such that supremum and integral cannot be interchanged

score 48 · Answer 15 · 2026-04-16 22:21:57

48

Views

$\int|f|^\alpha|g|^{1-\alpha}d\mu\le(\int|f|d\mu)^\alpha(\int|g|d\mu)^{1-\alpha}$

Published on 16 Apr 2026 - 22:21

List Question

Are there inner and outer approximation theorems for arbitrary measures?

probability density of a probability density of a probability density ... limiting distribution?

Continuity from below of outer measure extending an algebrea

Convergence of a sequence of measures of sets implies convergence of the indicator functions.

The proof of Caratheodory's criterion from Bogachev's book

Integral inequality of measurable functions for every measurable set implies function inequality a.e. as long as measure is $\sigma$-finite

Show that the market is arbitrage free if $a < S_0^1(1+r)< b$

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

Two Baire measure, $\left\{A\subseteq X: A \text{ Baire set}\ \mu(A)=\nu(A)\right\}$ is $\sigma$-algebra

A family of continuous distribution functions with a singular law to the Lebesgue measure

Why $\frac{dx}{|x|}$ is a Haar measure on $\mathbb{R}\setminus\{0\}$

Hausdorff measure (open subset containing x)

For which measures does the monotone convergence theorem hold?

Finding an increasing sequence of Lebesgue integrable functions such that supremum and integral cannot be interchanged

$\int|f|^\alpha|g|^{1-\alpha}d\mu\le(\int|f|d\mu)^\alpha(\int|g|d\mu)^{1-\alpha}$

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