Question

If $f_k\to f$ in measure, does $f_k\to f$?

score 95 · Answer 1 · 2026-04-15 03:59:13

95

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If $f_k\to f$ in measure, does $f_k\to f$?

Published on 15 Apr 2026 - 3:59

score 47 · Answer 2 · 2026-04-15 06:07:36

47

Views

Show that $f(x)=\int_{[a,x]} g \, dm$ is continuous on $[a,b]$

Published on 15 Apr 2026 - 6:07

score 121 · Answer 3 · 2026-04-16 22:18:11

121

Views

If $f:\mathbb{R}\to\mathbb{R}$ is Lebesgue integrable, then $\lim\limits_{t\to 0}\int_\mathbb{R}|f(x+t)-f(x)|dx=0.$

Published on 16 Apr 2026 - 22:18

score 77 · Answer 4 · 2026-04-11 14:42:52

77

Views

Riesz-Fischer Theorem with Variable Exponent

Published on 11 Apr 2026 - 14:42

score 122 · Answer 5 · 2026-04-13 19:42:43

122

Views

Showing Convergence of Positive Series

Published on 13 Apr 2026 - 19:42

score 62 · Answer 6 · 2026-04-11 22:29:04

62

Views

Existence of $L^{1}(\mathbb{R}^{n})$ Function Defined via Functional Equation

Published on 11 Apr 2026 - 22:29

score 1k · Answer 7 · 2026-04-11 19:04:22

1k

Views

Is the following function Lebesgue integrable?

Published on 11 Apr 2026 - 19:04

score 103 · Answer 8 · 2026-04-16 04:19:01

103

Views

Example when $\int \sum f_k d\mu \not = \sum_k \int f_k d\mu$ and $\sum_k f_k $ absolutely convergent

Published on 16 Apr 2026 - 4:19

score 124 · Answer 9 · 2026-04-12 17:15:06

124

Views

Showing Lebesgue's definition of measure implies measurability

Published on 12 Apr 2026 - 17:15

score 23 · Answer 10 · 2026-04-16 02:56:08

23

Views

Given $A\subset [0,1]$ prove that $m^(\{1-x:x\in A \})=m^ (A)$

Published on 16 Apr 2026 - 2:56

score 75 · Answer 11 · 2026-04-10 00:47:14

75

Views

Exponential growth as check for integrability

Published on 10 Apr 2026 - 0:47

score 124 · Answer 12 · 2026-04-12 06:43:44

124

Views

A positive measurable and improper integrable function is integrable

Published on 12 Apr 2026 - 6:43

score 696 · Answer 13 · 2026-04-15 02:52:52

696

Views

Determining two iterated integrals over the diagonal line of the cube $[0, 1]^2$

Published on 15 Apr 2026 - 2:52

score 848 · Answer 14 · 2026-04-15 10:49:54

848

Views

Examples of theorems from advanced calculus that are easier to prove with Lebesuge integral.

Published on 15 Apr 2026 - 10:49

score 147 · Answer 15 · 2026-04-16 23:09:45

147

Views

Calculate $ \lim _{n \rightarrow \infty }\int ^{n}_{-n} \left(\cos\left(\frac{x}{n}\right)\right)^{n^{2}}\,dx $

Published on 16 Apr 2026 - 23:09

List Question

If $f_k\to f$ in measure, does $f_k\to f$?

Show that $f(x)=\int_{[a,x]} g \, dm$ is continuous on $[a,b]$

If $f:\mathbb{R}\to\mathbb{R}$ is Lebesgue integrable, then $\lim\limits_{t\to 0}\int_\mathbb{R}|f(x+t)-f(x)|dx=0.$

Riesz-Fischer Theorem with Variable Exponent

Showing Convergence of Positive Series

Existence of $L^{1}(\mathbb{R}^{n})$ Function Defined via Functional Equation

Is the following function Lebesgue integrable?

Example when $\int \sum f_k d\mu \not = \sum_k \int f_k d\mu$ and $\sum_k f_k $ absolutely convergent

Showing Lebesgue's definition of measure implies measurability

Given $A\subset [0,1]$ prove that $m^(\{1-x:x\in A \})=m^ (A)$

Exponential growth as check for integrability

A positive measurable and improper integrable function is integrable

Determining two iterated integrals over the diagonal line of the cube $[0, 1]^2$

Examples of theorems from advanced calculus that are easier to prove with Lebesuge integral.

Calculate $ \lim _{n \rightarrow \infty }\int ^{n}_{-n} \left(\cos\left(\frac{x}{n}\right)\right)^{n^{2}}\,dx $

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