Question

How is the Lebesgue measure related to a Normal distributed random variable $x\sim N(\mu, \sigma^2)$?

score 88 · Answer 1 · 2026-04-23 11:20:04

88

Views

How is the Lebesgue measure related to a Normal distributed random variable $x\sim N(\mu, \sigma^2)$?

Published on 23 Apr 2026 - 11:20

score 43 · Answer 2 · 2026-04-13 14:11:57

43

Views

showing the function is uniformly continuous.

Published on 13 Apr 2026 - 14:11

score 67 · Answer 3 · 2026-04-11 17:03:05

67

Views

In Lebesgue's characterization of measurability, why is the set required to have finite outer measure?

Published on 11 Apr 2026 - 17:03

score 96 · Answer 4 · 2026-04-12 18:19:05

96

Views

Measure of the set of numbers in $[0,1]$ expressed with different quantities of zeroes and ones in binary

Published on 12 Apr 2026 - 18:19

score 32 · Answer 5 · 2026-04-15 04:46:16

32

Views

$L_1$ convergence, pointwise convergence and the supremum

Published on 15 Apr 2026 - 4:46

score 56 · Answer 6 · 2026-04-12 16:21:00

56

Views

Why the closed unit ball is the countable union of disjoint cells?

Published on 12 Apr 2026 - 16:21

score 29 · Answer 7 · 2026-04-14 01:11:40

29

Views

Equivalence of outer lebesgue measure if covering of cubes is required rather than cuboids

Published on 14 Apr 2026 - 1:11

score 100 · Answer 8 · 2026-04-12 20:36:00

100

Views

Showing the union of two measurable sets is measurable with the $G_\delta$ definition

Published on 12 Apr 2026 - 20:36

score 47 · Answer 9 · 2026-04-13 22:36:39

Let $A \subset \mathbb{R}^d, \ddot{A}$ be the interior of $A$ and $\bar{A}$ be the closure of $A$. Show: if $\lambda_d(\ddot{A})=\lambda_d(\bar{A})$

score 74 · Answer 10 · 2026-04-15 14:39:48

74

Views

$\nu(A)=m(f^{-1}(A))$ when $m$ Lebesgue measure and $f(x)=x^{3}$. Is $\nu<<m$?

Published on 15 Apr 2026 - 14:39

score 24 · Answer 11 · 2026-04-16 18:50:25

24

Views

Distance set of a Borel set is a Lebesgue set.

Published on 16 Apr 2026 - 18:50

score 46 · Answer 12 · 2026-04-16 03:00:03

46

Views

Hann decomposition problem, Let $\mu$ a finite measure, such that $\lambda \ll \mu$ and let $P_n, N_n$ Hann decomposition for $\lambda - n\mu$.

Published on 16 Apr 2026 - 3:00

score 109 · Answer 13 · 2026-04-16 07:52:36

109

Views

Which is greater - $\int_0^1\frac{1}{f(x)}dx$ or $\bigg(\int_0^1f(x)dx\bigg)^{-1}$?

Published on 16 Apr 2026 - 7:52

score 37 · Answer 14 · 2026-04-11 16:55:48

37

Views

A dense set of real numbers with predetermined Lebesgue measure

Published on 11 Apr 2026 - 16:55

score 110 · Answer 15 · 2026-04-09 04:21:18

110

Views

Is the Sum of Countable Increasing Continuous Functions also Continuous?

Published on 09 Apr 2026 - 4:21

List Question

How is the Lebesgue measure related to a Normal distributed random variable $x\sim N(\mu, \sigma^2)$?

showing the function is uniformly continuous.

In Lebesgue's characterization of measurability, why is the set required to have finite outer measure?

Measure of the set of numbers in $[0,1]$ expressed with different quantities of zeroes and ones in binary

$L_1$ convergence, pointwise convergence and the supremum

Why the closed unit ball is the countable union of disjoint cells?

Equivalence of outer lebesgue measure if covering of cubes is required rather than cuboids

Showing the union of two measurable sets is measurable with the $G_\delta$ definition

Let $A \subset \mathbb{R}^d, \ddot{A}$ be the interior of $A$ and $\bar{A}$ be the closure of $A$. Show: if $\lambda_d(\ddot{A})=\lambda_d(\bar{A})$

$\nu(A)=m(f^{-1}(A))$ when $m$ Lebesgue measure and $f(x)=x^{3}$. Is $\nu<<m$?

Distance set of a Borel set is a Lebesgue set.

Hann decomposition problem, Let $\mu$ a finite measure, such that $\lambda \ll \mu$ and let $P_n, N_n$ Hann decomposition for $\lambda - n\mu$.

Which is greater - $\int_0^1\frac{1}{f(x)}dx$ or $\bigg(\int_0^1f(x)dx\bigg)^{-1}$?

A dense set of real numbers with predetermined Lebesgue measure

Is the Sum of Countable Increasing Continuous Functions also Continuous?

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