Question

Let $f:\Xi\rightarrow\mathbb{R}$ we consider $F$ defined by $F(\nu):=\int_{\Xi}f(\xi)\nu(d\xi)$. Is $F$ continuous with respect to the metric $W_{p}$?

score 54 · Answer 1 · 2026-03-25 07:46:22

54

Views

Let $f:\Xi\rightarrow\mathbb{R}$ we consider $F$ defined by $F(\nu):=\int_{\Xi}f(\xi)\nu(d\xi)$. Is $F$ continuous with respect to the metric $W_{p}$?

Published on 25 Mar 2026 - 7:46

score 155 · Answer 2 · 2026-04-12 23:31:36

155

Views

The Integral of which the real part is the Poisson Integral of $f$, is Holomorphic

Published on 12 Apr 2026 - 23:31

score 235 · Answer 3 · 2026-03-25 06:11:23

235

Views

Prove that the set $[0,1]\setminus E$ has Lebesgue measure zero.

Published on 25 Mar 2026 - 6:11

score 38 · Answer 4 · 2026-03-26 17:50:23

38

Views

Integration of $F$-valued functions with respect to a $E$-valued measure and a bounded bilinear operator $E\times F→G$. How is this integral called?

Published on 26 Mar 2026 - 17:50

score 62 · Answer 5 · 2026-04-11 03:56:24

62

Views

Equivalence of convergence. In particular $L^p$ and in measure.

Published on 11 Apr 2026 - 3:56

score 214 · Answer 6 · 2026-04-12 13:35:07

214

Views

Show a sequence of densities converge to some density.

Published on 12 Apr 2026 - 13:35

score 395 · Answer 7 · 2026-04-10 20:10:12

395

Views

Why should a physicist care about measurability of random variables?

Published on 10 Apr 2026 - 20:10

score 22 · Answer 8 · 2026-04-11 18:05:11

22

Views

Randomly drawing a point on a specific line in a plain.

Published on 11 Apr 2026 - 18:05

score 175 · Answer 9 · 2026-04-12 16:57:03

175

Views

Prove that the zero set of a quadratic function has measure zero

Published on 12 Apr 2026 - 16:57

score 334 · Answer 10 · 2026-04-09 01:58:38

334

Views

The measurability of convolution in locally compact group

Published on 09 Apr 2026 - 1:58

score 108 · Answer 11 · 2026-04-09 07:29:16

108

Views

Lower semicontinuous submeasure is countably subadditive

Published on 09 Apr 2026 - 7:29

score 638 · Answer 12 · 2026-04-11 20:44:55

638

Views

Fubini's Theorem Application

Published on 11 Apr 2026 - 20:44

score 337 · Answer 13 · 2026-03-25 06:04:10

337

Views

f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

Published on 25 Mar 2026 - 6:04

score 161 · Answer 14 · 2026-03-29 04:34:44

161

Views

Bernoulli trials $X_1 , X_2 , X_3 , \ldots$

Published on 29 Mar 2026 - 4:34

score 250 · Answer 15 · 2026-04-09 01:47:36

250

Views

Is composition of a continuous function a continuous operator?

Published on 09 Apr 2026 - 1:47

List Question

Let $f:\Xi\rightarrow\mathbb{R}$ we consider $F$ defined by $F(\nu):=\int_{\Xi}f(\xi)\nu(d\xi)$. Is $F$ continuous with respect to the metric $W_{p}$?

The Integral of which the real part is the Poisson Integral of $f$, is Holomorphic

Prove that the set $[0,1]\setminus E$ has Lebesgue measure zero.

Integration of $F$-valued functions with respect to a $E$-valued measure and a bounded bilinear operator $E\times F→G$. How is this integral called?

Equivalence of convergence. In particular $L^p$ and in measure.

Show a sequence of densities converge to some density.

Why should a physicist care about measurability of random variables?

Randomly drawing a point on a specific line in a plain.

Prove that the zero set of a quadratic function has measure zero

The measurability of convolution in locally compact group

Lower semicontinuous submeasure is countably subadditive

Fubini's Theorem Application

f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

Bernoulli trials $X_1 , X_2 , X_3 , \ldots$

Is composition of a continuous function a continuous operator?

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