Question

$L^2$ norm on a product space $]0,1[\times \Omega$

score 150 · Answer 1 · 2026-04-12 16:09:17

150

Views

$L^2$ norm on a product space $]0,1[\times \Omega$

Published on 12 Apr 2026 - 16:09

score 37 · Answer 2 · 2026-04-10 16:40:08

37

Views

measurability of function that differs from continuous function

Published on 10 Apr 2026 - 16:40

score 252 · Answer 3 · 2026-04-15 07:54:02

252

Views

Generalized Egoroff's Theorem

Published on 15 Apr 2026 - 7:54

score 40 · Answer 4 · 2026-04-15 05:03:42

40

Views

Measurability of the following set

Published on 15 Apr 2026 - 5:03

score 187 · Answer 5 · 2026-04-17 11:08:36

187

Views

Showing an $L^2$ convergence (with convergence rate)

Published on 17 Apr 2026 - 11:08

score 50 · Answer 6 · 2026-04-17 01:45:03

50

Views

$ \varphi(x_1, \dots , x_n) = (c_1x_1, \dots, c_nx_n)$. Then, $\mu(\varphi(A)) = |c_1\dots c_n|\mu(A)$, where $\mu$ is the Lebesgue measure

Published on 17 Apr 2026 - 1:45

score 85 · Answer 7 · 2026-04-09 21:55:35

85

Views

How to take complements in sub-$\sigma$-algebra

Published on 09 Apr 2026 - 21:55

score 457 · Answer 8 · 2026-04-15 06:13:49

457

Views

Show the limit of the characteristic function is zero a.e.

Published on 15 Apr 2026 - 6:13

score 41 · Answer 9 · 2026-04-13 16:39:31

41

Views

How to understand the expression $\int_{t\in\mathcal{T}}Y(t)dI\{t\ge T\}$

Published on 13 Apr 2026 - 16:39

score 77 · Answer 10 · 2026-04-18 01:08:36

77

Views

Finding a function $f\in L^p \setminus L^q$ for $0<p<q<\infty$

Published on 18 Apr 2026 - 1:08

score 29 · Answer 11 · 2026-04-15 06:13:44

29

Views

$f(x) \in \mathcal{M} (\mathbb{R}, \mathfrak{B}) \Leftrightarrow g_y(x):=f(x+y) \in \mathcal{M} (\mathbb{R}, \mathfrak{B})$

Published on 15 Apr 2026 - 6:13

score 2.3k · Answer 12 · 2026-04-10 17:29:25

2.3k

Views

What does it mean that a probability distribution has full support?

Published on 10 Apr 2026 - 17:29

score 128 · Answer 13 · 2026-04-13 07:32:52

128

Views

Controlling this function in $L^2$ norm

Published on 13 Apr 2026 - 7:32

score 52 · Answer 14 · 2026-04-17 10:54:59

52

Views

If $|\partial f / \partial x | \leq g (y)$ for some $g $ show$ \frac {d}{dx} \int f dx = \int \partial f / \partial x dy $

Published on 17 Apr 2026 - 10:54

score 363 · Answer 15 · 2026-04-15 04:41:10

363

Views

Prove that if $f $ is $\alpha$-Hölder continuous with $\alpha > 1/2$, then the image of $f $ has measure zero in $\mathbb R^2$.

Published on 15 Apr 2026 - 4:41

List Question

$L^2$ norm on a product space $]0,1[\times \Omega$

measurability of function that differs from continuous function

Generalized Egoroff's Theorem

Measurability of the following set

Showing an $L^2$ convergence (with convergence rate)

$ \varphi(x_1, \dots , x_n) = (c_1x_1, \dots, c_nx_n)$. Then, $\mu(\varphi(A)) = |c_1\dots c_n|\mu(A)$, where $\mu$ is the Lebesgue measure

How to take complements in sub-$\sigma$-algebra

Show the limit of the characteristic function is zero a.e.

How to understand the expression $\int_{t\in\mathcal{T}}Y(t)dI\{t\ge T\}$

Finding a function $f\in L^p \setminus L^q$ for $0<p<q<\infty$

$f(x) \in \mathcal{M} (\mathbb{R}, \mathfrak{B}) \Leftrightarrow g_y(x):=f(x+y) \in \mathcal{M} (\mathbb{R}, \mathfrak{B})$

What does it mean that a probability distribution has full support?

Controlling this function in $L^2$ norm

If $|\partial f / \partial x | \leq g (y)$ for some $g $ show$ \frac {d}{dx} \int f dx = \int \partial f / \partial x dy $

Prove that if $f $ is $\alpha$-Hölder continuous with $\alpha > 1/2$, then the image of $f $ has measure zero in $\mathbb R^2$.

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