Question

Notation for defining a measure in terms of its density?

score 130 · Answer 1 · 2026-04-10 11:50:08

130

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Notation for defining a measure in terms of its density?

Published on 10 Apr 2026 - 11:50

score 809 · Answer 2 · 2026-04-15 00:44:19

809

Views

$ \int_0^af = 0, \forall a \in \mathbb{R} \Rightarrow f=0$ almost everywhere

Published on 15 Apr 2026 - 0:44

score 73 · Answer 3 · 2026-04-29 17:18:16

73

Views

Prove that $F$ is continuous function of $t$

Published on 29 Apr 2026 - 17:18

score 88 · Answer 4 · 2026-04-16 10:03:36

88

Views

Prove that $F'(x)=f(x)$, for almost all $x\in[0,1]$.

Published on 16 Apr 2026 - 10:03

score 72 · Answer 5 · 2026-04-14 00:21:32

72

Views

Product of integrable by bounded function (Daniell approach)

Published on 14 Apr 2026 - 0:21

score 572 · Answer 6 · 2026-04-14 22:59:50

572

Views

$L^1$ convergence and absolute continuity

Published on 14 Apr 2026 - 22:59

score 121 · Answer 7 · 2026-04-15 05:15:55

121

Views

Change of coordinates using Lebesgue area measure on $\mathbb C$

Published on 15 Apr 2026 - 5:15

score 284 · Answer 8 · 2026-04-15 22:06:47

284

Views

dominated convergence question: $\int_0^n (1-\frac{x}{n})^n \log(2+\cos(\frac{x}{n}))\mathrm dx$

Published on 15 Apr 2026 - 22:06

score 60 · Answer 9 · 2026-04-11 10:43:53

60

Views

Integration on $[0, \infty)$

Published on 11 Apr 2026 - 10:43

score 66 · Answer 10 · 2026-04-12 21:53:20

66

Views

Showing the following integral is 0.

Published on 12 Apr 2026 - 21:53

score 513 · Answer 11 · 2026-04-17 07:43:49

513

Views

Prove that if $(f_n)_{n=0}^\infty$ is a uniformly bounded sequence of measurable functions, then $f=\limsup f_n$ is measurable.

Published on 17 Apr 2026 - 7:43

score 132 · Answer 12 · 2026-04-15 00:55:27

132

Views

Counter example for $\int_\mathbb{R} f_nd\mu\rightarrow\int_\mathbb{R} fd\mu$

Published on 15 Apr 2026 - 0:55

score 212 · Answer 13 · 2026-04-15 21:23:28

212

Views

Let $f$ and $f'$ both be integrable on $\mathbb{R}$, show that $\int_{\mathbb{R}}f'(t)\mathrm dt=0$

Published on 15 Apr 2026 - 21:23

score 224 · Answer 14 · 2026-04-12 11:52:31

224

Views

asymmetric joint distributions with symmetric marginals

Published on 12 Apr 2026 - 11:52

score 137 · Answer 15 · 2026-03-26 16:06:59

137

Views

If $H$ is a Hilbert space with orthonormal basis $(e_n)$, then $X:\Omega\to H$ is integrable iff $\langle X,e_n\rangle$ is integrable for all $n$

Published on 26 Mar 2026 - 16:06

List Question

Notation for defining a measure in terms of its density?

$ \int_0^af = 0, \forall a \in \mathbb{R} \Rightarrow f=0$ almost everywhere

Prove that $F$ is continuous function of $t$

Prove that $F'(x)=f(x)$, for almost all $x\in[0,1]$.

Product of integrable by bounded function (Daniell approach)

$L^1$ convergence and absolute continuity

Change of coordinates using Lebesgue area measure on $\mathbb C$

dominated convergence question: $\int_0^n (1-\frac{x}{n})^n \log(2+\cos(\frac{x}{n}))\mathrm dx$

Integration on $[0, \infty)$

Showing the following integral is 0.

Prove that if $(f_n)_{n=0}^\infty$ is a uniformly bounded sequence of measurable functions, then $f=\limsup f_n$ is measurable.

Counter example for $\int_\mathbb{R} f_nd\mu\rightarrow\int_\mathbb{R} fd\mu$

Let $f$ and $f'$ both be integrable on $\mathbb{R}$, show that $\int_{\mathbb{R}}f'(t)\mathrm dt=0$

asymmetric joint distributions with symmetric marginals

If $H$ is a Hilbert space with orthonormal basis $(e_n)$, then $X:\Omega\to H$ is integrable iff $\langle X,e_n\rangle$ is integrable for all $n$

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