Question

Existence of a functional on $L^\infty$ that vanish on C(X)

score 443 · Answer 1 · 2026-03-25 14:34:33

443

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Existence of a functional on $L^\infty$ that vanish on C(X)

Published on 25 Mar 2026 - 14:34

score 231 · Answer 2 · 2026-03-26 03:01:29

231

Views

Is it possible to interchange the limit and the probability measure for trajectories of stochastic differential equation?

Published on 26 Mar 2026 - 3:01

score 264 · Answer 3 · 2019-11-16 13:04:46

264

Views

Show that: $f : \mathbb{R} → \mathbb{R} ; \ x \mapsto \cos^2(x)$ is measurable with respect to the Lebesgue measure space

Published on 16 Nov 2019 - 13:04

score 134 · Answer 4 · 2026-04-10 17:05:37

134

Views

$\lim_{n \to \infty} \int_E h_n = 0 \iff \{h_n \} $ is uniformly intergrable over $E$.

Published on 10 Apr 2026 - 17:05

score 101 · Answer 5 · 2026-04-10 10:22:44

101

Views

Continuous function over measurable set

Published on 10 Apr 2026 - 10:22

score 193 · Answer 6 · 2026-03-25 12:12:15

193

Views

Measurable function with parameters

Published on 25 Mar 2026 - 12:12

score 120 · Answer 7 · 2026-03-31 07:09:45

120

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For $\alpha$ irrational, prove that $F(x,y):=(x+\alpha\mod1,x+y\mod1)$, $T^{2}\to T^{2}$ preserves the Lebesgue measure.

Published on 31 Mar 2026 - 7:09

score 25 · Answer 8 · 2026-03-25 12:50:49

25

Views

If $\lim \int_0^1 |f_n(x)|=0$ and $|f_n|^2\leq g$ where g is integrable on [0,1], then $\lim \int_0^1 |f_n|^2=0$

Published on 25 Mar 2026 - 12:50

score 100 · Answer 9 · 2019-11-18 14:52:47

100

Views

Let $f$ be integrable over $R$ such that for any open set $U$: $\int_u fd\mu\leq b\mu(u)$. Then $f\leq b$ a.e

Published on 18 Nov 2019 - 14:52

score 56 · Answer 10 · 2026-04-10 18:04:42

56

Views

Lebesgue integral of $\int_\Omega fd\mu$ where $\mu(A)=\sum\limits_{k=1}^{n}\alpha_k\cdot\delta_{x_k}$

Published on 10 Apr 2026 - 18:04

score 137 · Answer 11 · 2026-04-10 23:56:42

137

Views

Does every set of Lebesgue measure greater than zero have an accumulation point?

Published on 10 Apr 2026 - 23:56

score 55 · Answer 12 · 2019-11-19 21:57:45

55

Views

$L^2$ and $L^1$ convergence

Published on 19 Nov 2019 - 21:57

score 453 · Answer 13 · 2019-11-20 23:33:01

453

Views

If $A \subset \mathbb{R^{n+m}}$ has Lebesgue measure zero then almost every section has measure zero.

Published on 20 Nov 2019 - 23:33

score 31 · Answer 14 · 2026-04-03 13:55:50

31

Views

how to show $\int|f|^{p} \mathrm{d} \mu=\sum_{n=1}^{\infty} \frac{\sqrt{n}^{p}}{n^{2}}$?

Published on 03 Apr 2026 - 13:55

score 33 · Answer 15 · 2026-04-03 13:54:05

33

Views

Proving that certain set has a maximun

Published on 03 Apr 2026 - 13:54

List Question

Existence of a functional on $L^\infty$ that vanish on C(X)

Is it possible to interchange the limit and the probability measure for trajectories of stochastic differential equation?

Show that: $f : \mathbb{R} → \mathbb{R} ; \ x \mapsto \cos^2(x)$ is measurable with respect to the Lebesgue measure space

$\lim_{n \to \infty} \int_E h_n = 0 \iff \{h_n \} $ is uniformly intergrable over $E$.

Continuous function over measurable set

Measurable function with parameters

For $\alpha$ irrational, prove that $F(x,y):=(x+\alpha\mod1,x+y\mod1)$, $T^{2}\to T^{2}$ preserves the Lebesgue measure.

If $\lim \int_0^1 |f_n(x)|=0$ and $|f_n|^2\leq g$ where g is integrable on [0,1], then $\lim \int_0^1 |f_n|^2=0$

Let $f$ be integrable over $R$ such that for any open set $U$: $\int_u fd\mu\leq b\mu(u)$. Then $f\leq b$ a.e

Lebesgue integral of $\int_\Omega fd\mu$ where $\mu(A)=\sum\limits_{k=1}^{n}\alpha_k\cdot\delta_{x_k}$

Does every set of Lebesgue measure greater than zero have an accumulation point?

$L^2$ and $L^1$ convergence

If $A \subset \mathbb{R^{n+m}}$ has Lebesgue measure zero then almost every section has measure zero.

how to show $\int|f|^{p} \mathrm{d} \mu=\sum_{n=1}^{\infty} \frac{\sqrt{n}^{p}}{n^{2}}$?

Proving that certain set has a maximun

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