Question

Prove or disprove the identity on $\sigma$-algebras

score 86 · Answer 1 · 2026-04-16 16:00:05

86

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Prove or disprove the identity on $\sigma$-algebras

Published on 16 Apr 2026 - 16:00

score 65 · Answer 2 · 2026-04-16 13:04:01

65

Views

If $\mu(A)>0$ forces $\mu(A)\geq1$ and $1\leq p<q<\infty$, then $L^p \subseteq L^q\subseteq L^\infty$ and $\|f\|_\infty\leq\|f\|_q\leq\|f\|_p$

Published on 16 Apr 2026 - 13:04

score 69 · Answer 3 · 2026-04-13 08:38:52

69

Views

Defining Existence of Lebesgue Integral , Hypothesis Changes

Published on 13 Apr 2026 - 8:38

score 31 · Answer 4 · 2026-04-16 05:42:33

31

Views

Is $\int_{\mathbb{R}^{d}}{e^{-d(x,C)}dP}$ finite?

Published on 16 Apr 2026 - 5:42

score 74 · Answer 5 · 2026-04-13 18:50:40

74

Views

How to define Lebesgue Integrability of functions assuming values in an arbitrary topological vector space over an arbitrary topological field?

Published on 13 Apr 2026 - 18:50

score 139 · Answer 6 · 2026-04-10 23:16:25

139

Views

Showing the density of a quotient of two independent random variables

Published on 10 Apr 2026 - 23:16

score 80 · Answer 7 · 2026-04-17 02:55:10

80

Views

Show that $\|f\|_{p}\leq \|f\|_{\infty}$ for any $0<p<\infty$ in a general measure space $X$ with $\mu(X)=1$.

Published on 17 Apr 2026 - 2:55

score 57 · Answer 8 · 2026-04-14 15:39:10

57

Views

Lebesgue measure of the set of differences in a Cantor-like set

Published on 14 Apr 2026 - 15:39

score 56 · Answer 9 · 2026-04-12 16:05:03

56

Views

What is the generated σ -Algebra?

Published on 12 Apr 2026 - 16:05

score 47 · Answer 10 · 2026-04-15 17:16:02

47

Views

Is $f(x)=\frac{\cos x}{\sqrt{x+1}}$ $\space$, $x\in(0,+\infty)$ Lebesgue integrable???

Published on 15 Apr 2026 - 17:16

score 52 · Answer 11 · 2026-04-13 16:17:26

52

Views

Construct a sequence of step function $f_k$ so that $f_k \rightarrow f$ a.e.

Published on 13 Apr 2026 - 16:17

score 76 · Answer 12 · 2026-04-17 15:35:02

76

Views

If $0\leq f_{n}\leq g_{n}$, $f_{n}\longrightarrow f$, $g_{n}\longrightarrow g$, $\int_{0}^{1}g{n}\longrightarrow \int_{0}^{1}g$, then so is $f_{n}$.

Published on 17 Apr 2026 - 15:35

score 77 · Answer 13 · 2026-04-16 06:02:53

77

Views

Why Luzin's theorem can not be changed from $|\mathbb{R} \backslash B| < \epsilon$ to $|\mathbb{R} \backslash B| = 0$

Published on 16 Apr 2026 - 6:02

score 432 · Answer 14 · 2026-04-11 22:21:04

432

Views

Proof Verification: Bartle's "Elements of Integration" - Exercise 4.S

Published on 11 Apr 2026 - 22:21

score 112 · Answer 15 · 2026-04-16 11:50:32

112

Views

Sum of integrals of $|g_i|<\infty$ implies $g_i$ converges to $0$, and there exists a set whose complement is zero

Published on 16 Apr 2026 - 11:50

List Question

Prove or disprove the identity on $\sigma$-algebras

If $\mu(A)>0$ forces $\mu(A)\geq1$ and $1\leq p<q<\infty$, then $L^p \subseteq L^q\subseteq L^\infty$ and $\|f\|_\infty\leq\|f\|_q\leq\|f\|_p$

Defining Existence of Lebesgue Integral , Hypothesis Changes

Is $\int_{\mathbb{R}^{d}}{e^{-d(x,C)}dP}$ finite?

How to define Lebesgue Integrability of functions assuming values in an arbitrary topological vector space over an arbitrary topological field?

Showing the density of a quotient of two independent random variables

Show that $\|f\|_{p}\leq \|f\|_{\infty}$ for any $0<p<\infty$ in a general measure space $X$ with $\mu(X)=1$.

Lebesgue measure of the set of differences in a Cantor-like set

What is the generated σ -Algebra?

Is $f(x)=\frac{\cos x}{\sqrt{x+1}}$ $\space$, $x\in(0,+\infty)$ Lebesgue integrable???

Construct a sequence of step function $f_k$ so that $f_k \rightarrow f$ a.e.

If $0\leq f_{n}\leq g_{n}$, $f_{n}\longrightarrow f$, $g_{n}\longrightarrow g$, $\int_{0}^{1}g{n}\longrightarrow \int_{0}^{1}g$, then so is $f_{n}$.

Why Luzin's theorem can not be changed from $|\mathbb{R} \backslash B| < \epsilon$ to $|\mathbb{R} \backslash B| = 0$

Proof Verification: Bartle's "Elements of Integration" - Exercise 4.S

Sum of integrals of $|g_i|<\infty$ implies $g_i$ converges to $0$, and there exists a set whose complement is zero

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