Question

Let $A_1, A_2, ..., A_n$ be a sequence of disjoint elementary sets. If $A = \cup A_i$ is elementary, then $m'(A) = \sum_{i = 1}^\infty m'(A_i)$

score 32 · Answer 1 · 2026-04-16 01:36:03

Let $A_1, A_2, ..., A_n$ be a sequence of disjoint elementary sets. If $A = \cup A_i$ is elementary, then $m'(A) = \sum_{i = 1}^\infty m'(A_i)$

score 41 · Answer 2 · 2026-04-12 07:02:58

41

Views

Relationship between dense sets, open sets and Lebesgue measure

Published on 12 Apr 2026 - 7:02

score 26 · Answer 3 · 2026-04-12 12:35:52

26

Views

Expectation of a function with respect to $\mu$ is zero, implies function is $\mu$-almost surely zero

Published on 12 Apr 2026 - 12:35

score 117 · Answer 4 · 2026-04-16 10:02:11

117

Views

The value of $\langle p^2 \rangle$ for $\psi(x)=e^{-|x|}$, where $\hat{p}:=i\frac{d}{dx}$ is the momentum operator.

Published on 16 Apr 2026 - 10:02

score 85 · Answer 5 · 2026-04-14 05:20:11

85

Views

Can anyone explain the relationship among limsup, inf and sup in this proof?

Published on 14 Apr 2026 - 5:20

score 52 · Answer 6 · 2026-04-12 05:58:19

52

Views

Sum of measures is less than measure of sum

Published on 12 Apr 2026 - 5:58

score 860 · Answer 7 · 2026-04-12 08:30:06

860

Views

Does a non-measurable set that is not contained in a null set always contain a set of positive measure?

Published on 12 Apr 2026 - 8:30

score 53 · Answer 8 · 2026-04-17 14:39:09

53

Views

Example of sequence of integrable maps such that integral smaller than $1/n$ but doesn't converge to zero almost everywhere

Published on 17 Apr 2026 - 14:39

score 56 · Answer 9 · 2026-03-25 23:16:04

56

Views

A bounded measurable function

Published on 25 Mar 2026 - 23:16

score 37 · Answer 10 · 2026-04-12 12:30:46

37

Views

What does this notation mean in the context of probability theory?

Published on 12 Apr 2026 - 12:30

score 72 · Answer 11 · 2026-04-15 22:50:01

72

Views

Lebesgue measure of $\{(x, y, z) \in \mathbb{R^3}: 2x^2 - y^2 + z^2 \le 2z, |y| \le 1\}$

Published on 15 Apr 2026 - 22:50

score 93 · Answer 12 · 2026-04-13 12:04:42

93

Views

Lebesgue measure of $\{(x, y, z) \in \mathbb{R^3}: ax^2 + y^2 \le 1, |z| + |y| \le 2\}$

Published on 13 Apr 2026 - 12:04

score 74 · Answer 13 · 2026-04-09 10:14:13

74

Views

When are two measures absolutely continuous?

Published on 09 Apr 2026 - 10:14

score 41 · Answer 14 · 2026-04-13 14:25:19

41

Views

A non-Borel Lebesgue measurable set hat is a subset of a measurable zero Borel st

Published on 13 Apr 2026 - 14:25

score 86 · Answer 15 · 2026-04-15 23:51:14

86

Views

$\lim_{{n \to \infty}} \int_{{\frac{1}{n^2}}}^{{n}} (n^2x - 1)e^{-n^2x^2} \,dx$

Published on 15 Apr 2026 - 23:51

List Question

Let $A_1, A_2, ..., A_n$ be a sequence of disjoint elementary sets. If $A = \cup A_i$ is elementary, then $m'(A) = \sum_{i = 1}^\infty m'(A_i)$

Relationship between dense sets, open sets and Lebesgue measure

Expectation of a function with respect to $\mu$ is zero, implies function is $\mu$-almost surely zero

The value of $\langle p^2 \rangle$ for $\psi(x)=e^{-|x|}$, where $\hat{p}:=i\frac{d}{dx}$ is the momentum operator.

Can anyone explain the relationship among limsup, inf and sup in this proof?

Sum of measures is less than measure of sum

Does a non-measurable set that is not contained in a null set always contain a set of positive measure?

Example of sequence of integrable maps such that integral smaller than $1/n$ but doesn't converge to zero almost everywhere

A bounded measurable function

What does this notation mean in the context of probability theory?

Lebesgue measure of $\{(x, y, z) \in \mathbb{R^3}: 2x^2 - y^2 + z^2 \le 2z, |y| \le 1\}$

Lebesgue measure of $\{(x, y, z) \in \mathbb{R^3}: ax^2 + y^2 \le 1, |z| + |y| \le 2\}$

When are two measures absolutely continuous?

A non-Borel Lebesgue measurable set hat is a subset of a measurable zero Borel st

$\lim_{{n \to \infty}} \int_{{\frac{1}{n^2}}}^{{n}} (n^2x - 1)e^{-n^2x^2} \,dx$

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