Question

Conditions of Fubini's theorem

score 216 · Answer 1 · 2026-04-29 21:00:51

216

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Conditions of Fubini's theorem

Published on 29 Apr 2026 - 21:00

score 35 · Answer 2 · 2026-04-25 09:52:21

35

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How to prove lim $x\int \frac{f(t)}{(t)}dt$ from $x \to 1$ as $x\to 0^{+} = 0$ , as $f\in L[0,1]$?

Published on 25 Apr 2026 - 9:52

score 1.1k · Answer 3 · 2026-04-14 14:08:13

1.1k

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Prove $P(X=Y) = 0$ when $X$ and $Y$ are two random variables on the same probability space.

Published on 14 Apr 2026 - 14:08

score 317 · Answer 4 · 2026-03-31 05:30:45

317

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Martingale and heat equation: a check one the martingale property

Published on 31 Mar 2026 - 5:30

score 434 · Answer 5 · 2026-04-04 03:06:03

434

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contradiction to Fubini's theorem

Published on 04 Apr 2026 - 3:06

score 58 · Answer 6 · 2026-04-14 23:34:58

58

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Justify the use of Fubini in the case where the product space includes $\Omega$

Published on 14 Apr 2026 - 23:34

score 79 · Answer 7 · 2026-03-26 06:22:24

79

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Proving that $\mathbb E\left[\sum\limits_{k=1}^\infty Z_k\frac{\sqrt 2\sin(k\pi t)}{k \pi}\right] = 0$ (for i.i.d. $Z_k\sim N(0,1)$)

Published on 26 Mar 2026 - 6:22

score 96 · Answer 8 · 2026-04-12 08:04:40

96

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Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?

Published on 12 Apr 2026 - 8:04

score 160 · Answer 9 · 2026-04-11 16:14:58

160

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Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?(2)

Published on 11 Apr 2026 - 16:14

score 110 · Answer 10 · 2026-03-25 07:46:23

110

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$\sum_{(s,t)\in S\times T} f(s,t)=\sum_{s\in S}\sum_{t\in T} f(s,t)$ via Fubini-Tonelli?

Published on 25 Mar 2026 - 7:46

score 94 · Answer 11 · 2026-04-02 20:36:17

94

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An example of $\int_{X \times Y} f d(\mu \times \lambda )$ is finite but such that $\int_{Y} f_{x} d\lambda $ is infinite for some $x \in (0,1).$

Published on 02 Apr 2026 - 20:36

score 130 · Answer 12 · 2026-03-25 14:22:40

130

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Proving something similar to $\mathbb E(g(X)) = \int_0^\infty g'(x) P(X>x) dP$

Published on 25 Mar 2026 - 14:22

score 84 · Answer 13 · 2020-03-12 03:54:10

84

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Show that an infinite Integral equals an infinite sum

Published on 12 Mar 2020 - 3:54

score 106 · Answer 14 · 2026-04-08 06:11:11

106

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Evaluate $\sum_{r=1}^{\infty} \frac{1 \cdot 3 \cdot \ldots (2r-1)}{r!}\left(\frac{2}{5} \right)^{r}$

Published on 08 Apr 2026 - 6:11

score 307 · Answer 15 · 2026-04-09 08:09:49

307

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(c) Calculate the homotopy fibre of the inclusion $i_{X} : X \vee X \rightarrow X \times X. $

Published on 09 Apr 2026 - 8:09

List Question

Conditions of Fubini's theorem

How to prove lim $x\int \frac{f(t)}{(t)}dt$ from $x \to 1$ as $x\to 0^{+} = 0$ , as $f\in L[0,1]$?

Prove $P(X=Y) = 0$ when $X$ and $Y$ are two random variables on the same probability space.

Martingale and heat equation: a check one the martingale property

contradiction to Fubini's theorem

Justify the use of Fubini in the case where the product space includes $\Omega$

Proving that $\mathbb E\left[\sum\limits_{k=1}^\infty Z_k\frac{\sqrt 2\sin(k\pi t)}{k \pi}\right] = 0$ (for i.i.d. $Z_k\sim N(0,1)$)

Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?

Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?(2)

$\sum_{(s,t)\in S\times T} f(s,t)=\sum_{s\in S}\sum_{t\in T} f(s,t)$ via Fubini-Tonelli?

An example of $\int_{X \times Y} f d(\mu \times \lambda )$ is finite but such that $\int_{Y} f_{x} d\lambda $ is infinite for some $x \in (0,1).$

Proving something similar to $\mathbb E(g(X)) = \int_0^\infty g'(x) P(X>x) dP$

Show that an infinite Integral equals an infinite sum

Evaluate $\sum_{r=1}^{\infty} \frac{1 \cdot 3 \cdot \ldots (2r-1)}{r!}\left(\frac{2}{5} \right)^{r}$

(c) Calculate the homotopy fibre of the inclusion $i_{X} : X \vee X \rightarrow X \times X. $

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