Question

If $f(x,s)$ is continuous on $s$ a.e. and measurable on $x$ for all $s$, how to show that $f$ is measurable in the product $\sigma$-algebra?

score 108 · Answer 1 · 2026-04-15 14:47:40

108

Views

If $f(x,s)$ is continuous on $s$ a.e. and measurable on $x$ for all $s$, how to show that $f$ is measurable in the product $\sigma$-algebra?

Published on 15 Apr 2026 - 14:47

score 68 · Answer 2 · 2026-04-13 06:40:17

68

Views

Joint Continuity of the Lebesgue Integral

Published on 13 Apr 2026 - 6:40

score 66 · Answer 3 · 2026-04-13 23:59:01

66

Views

Does this "averaging" function reproduce the same function in $L^1$?

Published on 13 Apr 2026 - 23:59

score 42 · Answer 4 · 2026-04-11 05:20:15

42

Views

About function satisfying an identity involving its $L_2$ norm

Published on 11 Apr 2026 - 5:20

score 224 · Answer 5 · 2026-04-14 02:57:09

224

Views

Show that union of line segments defined by a continuous function is Lebesgue measurable

Published on 14 Apr 2026 - 2:57

score 70 · Answer 6 · 2026-04-11 13:35:30

70

Views

Fremlin Question 132Xh

Published on 11 Apr 2026 - 13:35

score 44 · Answer 7 · 2026-04-09 17:04:01

44

Views

Measurability question about measure dependent on variables

Published on 09 Apr 2026 - 17:04

score 107 · Answer 8 · 2026-04-16 11:33:59

107

Views

Show that: $ \sum_{n\geq 1}{\frac{1}{n}(f_n(\omega)-g_n(\omega))}<\infty\qquad a.e $

Published on 16 Apr 2026 - 11:33

score 161 · Answer 9 · 2026-04-14 14:05:21

161

Views

Measurable function $f: \mathbb{R} \to (0,\infty)$ with $\int \chi_If d\lambda = \infty$ for every open interval of $\mathbb{R}$

Published on 14 Apr 2026 - 14:05

score 333 · Answer 10 · 2026-04-12 07:46:01

333

Views

Using monotone convergence theorem to find limit of integral

Published on 12 Apr 2026 - 7:46

score 103 · Answer 11 · 2026-04-16 04:09:21

103

Views

Show that $∫_E f=\lim ∫_E f_k $For any measurable set E .

Published on 16 Apr 2026 - 4:09

score 128 · Answer 12 · 2026-04-15 21:54:21

128

Views

$f(x+1/n)\to f$ in $L^1(\mathbb{R})$

Published on 15 Apr 2026 - 21:54

score 556 · Answer 13 · 2026-04-15 10:43:27

556

Views

What is the Lebesgue Measure of the set of numbers in (0,1) that contain 100 consecutve 4's?

Published on 15 Apr 2026 - 10:43

score 539 · Answer 14 · 2026-04-13 09:46:52

539

Views

Can a Non-Measurable Set be Approximated by Closed Sets from Below?

Published on 13 Apr 2026 - 9:46

score 861 · Answer 15 · 2026-04-16 20:20:11

861

Views

How to prove Lebesgue Measure is dilation-invariant for any B borel set

Published on 16 Apr 2026 - 20:20

List Question

If $f(x,s)$ is continuous on $s$ a.e. and measurable on $x$ for all $s$, how to show that $f$ is measurable in the product $\sigma$-algebra?

Joint Continuity of the Lebesgue Integral

Does this "averaging" function reproduce the same function in $L^1$?

About function satisfying an identity involving its $L_2$ norm

Show that union of line segments defined by a continuous function is Lebesgue measurable

Fremlin Question 132Xh

Measurability question about measure dependent on variables

Show that: $ \sum_{n\geq 1}{\frac{1}{n}(f_n(\omega)-g_n(\omega))}<\infty\qquad a.e $

Measurable function $f: \mathbb{R} \to (0,\infty)$ with $\int \chi_If d\lambda = \infty$ for every open interval of $\mathbb{R}$

Using monotone convergence theorem to find limit of integral

Show that $∫_E f=\lim ∫_E f_k $For any measurable set E .

$f(x+1/n)\to f$ in $L^1(\mathbb{R})$

What is the Lebesgue Measure of the set of numbers in (0,1) that contain 100 consecutve 4's?

Can a Non-Measurable Set be Approximated by Closed Sets from Below?

How to prove Lebesgue Measure is dilation-invariant for any B borel set

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