Question

How to show a function is Lebesgue measurable.

score 180 · Answer 1 · 2019-02-28 05:38:13

180

Views

How to show a function is Lebesgue measurable.

Published on 28 Feb 2019 - 5:38

score 729 · Answer 2 · 2019-02-28 08:32:45

729

Views

Simple function iff Lebesgue measurable and has finite range.

Published on 28 Feb 2019 - 8:32

score 64 · Answer 3 · 2026-03-25 17:10:11

64

Views

Prove measurability of the set of lines starting from measurable set.

Published on 25 Mar 2026 - 17:10

score 112 · Answer 4 · 2019-02-28 11:49:12

112

Views

Prove: $m(A)=0 \iff m^(A\cup B)=m^(B)$

Published on 28 Feb 2019 - 11:49

score 82 · Answer 5 · 2026-03-25 15:53:37

82

Views

Is the function $\displaystyle\liminf_{t\to t_0}f_t(x)$ Lebesgue measurable?

Published on 25 Mar 2026 - 15:53

score 110 · Answer 6 · 2026-03-29 07:34:33

110

Views

If $f_n\rightarrow f$ in $L^p$-norm, $1\leq p<\infty$, then $\lim\limits_{n\rightarrow\infty}m(\{x\in\mathbb{R}^d:|f_n(x)-f(x)|>\varepsilon\})=0$

Published on 29 Mar 2026 - 7:34

score 77 · Answer 7 · 2019-03-02 16:33:00

77

Views

Implicit function or measurable extension of a measurable selector

Published on 02 Mar 2019 - 16:33

score 23 · Answer 8 · 2019-03-02 17:52:52

23

Views

Replacing a sequence $u_n \rightarrow u$, in $L^2$ by a sequence compactly supported.

Published on 02 Mar 2019 - 17:52

score 101 · Answer 9 · 2026-03-29 07:32:55

101

Views

Find a sequence $(f_n)_n$ convergent in $L^{p}(\mathbb{R}^d)$ s.t. $\lim\limits_{n\rightarrow\infty}f_n(x)$ doesn't exist for a.e. $x\in\mathbb{R}^d$.

Published on 29 Mar 2026 - 7:32

score 536 · Answer 10 · 2026-03-25 11:22:57

536

Views

Can a non-measurable set be measurable? (Seriously)

Published on 25 Mar 2026 - 11:22

score 484 · Answer 11 · 2019-03-05 23:55:49

484

Views

Show that for any $\alpha\in (0,\lambda(E))$, there exists a measurable set $F\subset E$ such that $\lambda(F)=\alpha$.

Published on 05 Mar 2019 - 23:55

score 105 · Answer 12 · 2019-03-08 14:36:45

105

Views

Pushforward Measure Continuously Differentiable Function

Published on 08 Mar 2019 - 14:36

score 159 · Answer 13 · 2019-03-08 20:26:59

159

Views

How can a function(measure) be countably additive on a non sigma-ring

Published on 08 Mar 2019 - 20:26

score 211 · Answer 14 · 2026-03-29 10:48:57

211

Views

If $f:\mathbb{R} \to [0,\infty)$ is Lebesgue measurable and $\int_{(n,n+1]}f dm = 0$ for all $n \in \mathbb{Z}$, then $\int_E fdm =0$ for all $E$.

Published on 29 Mar 2026 - 10:48

score 88 · Answer 15 · 2026-03-29 09:11:34

88

Views

Rectifiable curves in $\mathbb{R}^n$ have measure $0$, but line integral is nonzero.

Published on 29 Mar 2026 - 9:11

List Question

How to show a function is Lebesgue measurable.

Simple function iff Lebesgue measurable and has finite range.

Prove measurability of the set of lines starting from measurable set.

Prove: $m(A)=0 \iff m^(A\cup B)=m^(B)$

Is the function $\displaystyle\liminf_{t\to t_0}f_t(x)$ Lebesgue measurable?

If $f_n\rightarrow f$ in $L^p$-norm, $1\leq p<\infty$, then $\lim\limits_{n\rightarrow\infty}m(\{x\in\mathbb{R}^d:|f_n(x)-f(x)|>\varepsilon\})=0$

Implicit function or measurable extension of a measurable selector

Replacing a sequence $u_n \rightarrow u$, in $L^2$ by a sequence compactly supported.

Find a sequence $(f_n)_n$ convergent in $L^{p}(\mathbb{R}^d)$ s.t. $\lim\limits_{n\rightarrow\infty}f_n(x)$ doesn't exist for a.e. $x\in\mathbb{R}^d$.

Can a non-measurable set be measurable? (Seriously)

Show that for any $\alpha\in (0,\lambda(E))$, there exists a measurable set $F\subset E$ such that $\lambda(F)=\alpha$.

Pushforward Measure Continuously Differentiable Function

How can a function(measure) be countably additive on a non sigma-ring

If $f:\mathbb{R} \to [0,\infty)$ is Lebesgue measurable and $\int_{(n,n+1]}f dm = 0$ for all $n \in \mathbb{Z}$, then $\int_E fdm =0$ for all $E$.

Rectifiable curves in $\mathbb{R}^n$ have measure $0$, but line integral is nonzero.

Trending Questions

Popular # Hahtags

Popular Questions