Question

If $f$ is locally a.e. constant in domain $\Omega$, then $f$ is constant a.e. in $\Omega$

score 97 · Answer 1 · 2026-04-28 12:20:35

97

Views

If $f$ is locally a.e. constant in domain $\Omega$, then $f$ is constant a.e. in $\Omega$

Published on 28 Apr 2026 - 12:20

score 17 · Answer 2 · 2026-04-12 19:38:57

17

Views

What's the measure of $A=\cap_{i=1}^\infty A_i$ for a monotone class when $A_i=\infty$ for all $i$

Published on 12 Apr 2026 - 19:38

score 110 · Answer 3 · 2026-04-12 13:21:19

110

Views

intuitively obvious integration identity

Published on 12 Apr 2026 - 13:21

score 114 · Answer 4 · 2026-04-14 00:26:19

114

Views

Interpretation of Tail Event

Published on 14 Apr 2026 - 0:26

score 65 · Answer 5 · 2026-04-16 09:27:56

65

Views

Why $\mathbb P\{\forall t, X_t=Y_t\}=1$ doesn't really make sense?

Published on 16 Apr 2026 - 9:27

score 45 · Answer 6 · 2026-04-16 15:07:28

45

Views

Prove that $\mathscr{F} = \sigma(\{f_\lambda^{-1}(B):\;\lambda \in \Lambda,\;B \in \mathscr{F}'\})$.

Published on 16 Apr 2026 - 15:07

score 153 · Answer 7 · 2026-03-25 09:27:35

153

Views

relation between the Lebesgue measure and the perimeter of a set

Published on 25 Mar 2026 - 9:27

score 45 · Answer 8 · 2026-04-12 00:23:28

45

Views

Define two sequences of i.i.d random variables

Published on 12 Apr 2026 - 0:23

score 109 · Answer 9 · 2026-04-15 17:11:47

109

Views

Integral list w. r. t. measure?

Published on 15 Apr 2026 - 17:11

score 153 · Answer 10 · 2026-04-12 17:16:10

153

Views

Definition of 'liminf' of sequence of sets in terms of indicator functions

Published on 12 Apr 2026 - 17:16

score 36 · Answer 11 · 2026-04-28 13:47:49

36

Views

Criterion for a subset lie inside a sigma algebra

Published on 28 Apr 2026 - 13:47

score 54 · Answer 12 · 2026-04-17 04:04:21

Suppose that $f_{n}$ decrease in measure. Show that $m(\limsup_{n \to \infty}\{f_{n} > \epsilon\}) = 0$ and that $f_{n} \to 0$ a.e.

score 5.5k · Answer 13 · 2026-04-17 08:13:02

5.5k

Views

Reverse Holder Inequality $\|fg\|_1\geq\| f\|_{\frac{1}{p}}\|g\|_{-\frac{1}{p-1}}$

Published on 17 Apr 2026 - 8:13

score 951 · Answer 14 · 2026-04-11 22:25:47

951

Views

What is the meaning of $d\mu$?

Published on 11 Apr 2026 - 22:25

score 34 · Answer 15 · 2026-04-12 16:37:44

34

Views

A question about convergence. Is it possible to find a subsequence increasing in this situation?

Published on 12 Apr 2026 - 16:37

List Question

If $f$ is locally a.e. constant in domain $\Omega$, then $f$ is constant a.e. in $\Omega$

What's the measure of $A=\cap_{i=1}^\infty A_i$ for a monotone class when $A_i=\infty$ for all $i$

intuitively obvious integration identity

Interpretation of Tail Event

Why $\mathbb P\{\forall t, X_t=Y_t\}=1$ doesn't really make sense?

Prove that $\mathscr{F} = \sigma(\{f_\lambda^{-1}(B):\;\lambda \in \Lambda,\;B \in \mathscr{F}'\})$.

relation between the Lebesgue measure and the perimeter of a set

Define two sequences of i.i.d random variables

Integral list w. r. t. measure?

Definition of 'liminf' of sequence of sets in terms of indicator functions

Criterion for a subset lie inside a sigma algebra

Suppose that $f_{n}$ decrease in measure. Show that $m(\limsup_{n \to \infty}\{f_{n} > \epsilon\}) = 0$ and that $f_{n} \to 0$ a.e.

Reverse Holder Inequality $\|fg\|_1\geq\| f\|_{\frac{1}{p}}\|g\|_{-\frac{1}{p-1}}$

What is the meaning of $d\mu$?

A question about convergence. Is it possible to find a subsequence increasing in this situation?

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