Question

$L^1 \subseteq L^2$?

score 177 · Answer 1 · 2026-04-10 21:49:15

177

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$L^1 \subseteq L^2$?

Published on 10 Apr 2026 - 21:49

score 2.7k · Answer 2 · 2026-03-24 23:51:02

2.7k

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Chebyshev's Inequality for conditional expectation

Published on 24 Mar 2026 - 23:51

score 512 · Answer 3 · 2026-04-10 16:54:06

512

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Limit of Convolution of functions

Published on 10 Apr 2026 - 16:54

score 59 · Answer 4 · 2026-04-09 17:08:59

59

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Equality of integrals on a measure space with group structure

Published on 09 Apr 2026 - 17:08

score 78 · Answer 5 · 2026-04-09 00:33:33

78

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A sequence $f_k:\Omega\rightarrow \mathbb R$ such that $\int f_k=0 \quad \forall k\in \mathbb N $ and $\lim\limits_{k\to\infty} f_k \equiv1$.

Published on 09 Apr 2026 - 0:33

score 108 · Answer 6 · 2018-02-15 19:33:20

108

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How can we show that $\mu\ll\nu$ iff $\lim_{\nu(S)\to0}\mu(S)=0$?

Published on 15 Feb 2018 - 19:33

score 92 · Answer 7 · 2026-03-25 04:43:34

92

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Do all measure zero sets belong to the measure space: If $\mu(N_1) = 0$ then is $N_1 \in \mathcal{M}_{\mu}$?

Published on 25 Mar 2026 - 4:43

score 155 · Answer 8 · 2018-02-16 00:31:18

155

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Equivalences of a tight sequence of probability measures on $\mathbb{R}^{k}$

Published on 16 Feb 2018 - 0:31

score 67 · Answer 9 · 2018-02-16 02:38:53

67

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Product of probability measures $\mu_{n}\nu_{n}\implies\mu\nu$ if and only if $\mu_{n}\implies\mu$ and $\nu_{n}\implies\nu$

Published on 16 Feb 2018 - 2:38

score 546 · Answer 10 · 2018-02-16 12:22:48

546

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Why isn't minimal sigma-algebra simply the set containing all countable unions and complements

Published on 16 Feb 2018 - 12:22

score 141 · Answer 11 · 2026-04-09 02:51:14

141

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logarithmic potential gives out a constant integral over an absolutely continuous measure

Published on 09 Apr 2026 - 2:51

score 29 · Answer 12 · 2026-04-12 06:28:14

29

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Notations in book

Published on 12 Apr 2026 - 6:28

score 422 · Answer 13 · 2018-02-16 15:45:46

Why $\sup_{\|f\|_2=1}(\left|\int_X \phi_1 |f|^2d\mu\right |^2 + \left|\int_X \phi_2 |f|^2d\mu\right |^2 )\ge ||\,|\phi_1|^2+|\phi_2|^2||_\infty\;?$

score 48 · Answer 14 · 2026-04-11 07:53:56

48

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On stopping times in continuous time

Published on 11 Apr 2026 - 7:53

score 117 · Answer 15 · 2026-03-25 04:40:28

117

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$\lim_{n \to \infty}[n,+\infty)$ has Lebesgue measure 0?

Published on 25 Mar 2026 - 4:40

List Question

$L^1 \subseteq L^2$?

Chebyshev's Inequality for conditional expectation

Limit of Convolution of functions

Equality of integrals on a measure space with group structure

A sequence $f_k:\Omega\rightarrow \mathbb R$ such that $\int f_k=0 \quad \forall k\in \mathbb N $ and $\lim\limits_{k\to\infty} f_k \equiv1$.

How can we show that $\mu\ll\nu$ iff $\lim_{\nu(S)\to0}\mu(S)=0$?

Do all measure zero sets belong to the measure space: If $\mu(N_1) = 0$ then is $N_1 \in \mathcal{M}_{\mu}$?

Equivalences of a tight sequence of probability measures on $\mathbb{R}^{k}$

Product of probability measures $\mu_{n}\nu_{n}\implies\mu\nu$ if and only if $\mu_{n}\implies\mu$ and $\nu_{n}\implies\nu$

Why isn't minimal sigma-algebra simply the set containing all countable unions and complements

logarithmic potential gives out a constant integral over an absolutely continuous measure

Notations in book

Why $\sup_{\|f\|_2=1}(\left|\int_X \phi_1 |f|^2d\mu\right |^2 + \left|\int_X \phi_2 |f|^2d\mu\right |^2 )\ge ||\,|\phi_1|^2+|\phi_2|^2||_\infty\;?$

On stopping times in continuous time

$\lim_{n \to \infty}[n,+\infty)$ has Lebesgue measure 0?

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