Question

If f is a measurable function with $\int_{[0,1]}(f(x))^{2} dm(x) < \infty$ then $\int_{[0,1]}|f(x)| dm(x) < \infty$.

score 196 · Answer 1 · 2019-06-02 14:29:40

196

Views

If f is a measurable function with $\int_{[0,1]}(f(x))^{2} dm(x) < \infty$ then $\int_{[0,1]}|f(x)| dm(x) < \infty$.

Published on 02 Jun 2019 - 14:29

score 262 · Answer 2 · 2019-06-03 02:32:40

262

Views

Integral of bounded measurable function with convergent sequence of measures.

Published on 03 Jun 2019 - 2:32

score 62 · Answer 3 · 2019-06-03 14:42:16

62

Views

If $f$ is integrable, does $\int f = \lim \int f_n$ hold?

Published on 03 Jun 2019 - 14:42

score 1k · Answer 4 · 2019-06-03 17:03:54

1k

Views

Calculating $ \lim_{n \rightarrow \infty} \int_{[0, \infty)} \frac{\sin(e^x) }{1+nx^2}\,dx$

Published on 03 Jun 2019 - 17:03

score 71 · Answer 5 · 2019-06-03 18:22:46

71

Views

Calculating $ \lim_{n \rightarrow \infty} \int_{[1, \infty)} \frac{n \sin(\frac{x}{n}) }{x^3}\,dx$

Published on 03 Jun 2019 - 18:22

score 492 · Answer 6 · 2019-06-04 14:39:30

492

Views

How to calculate an integral given a measure?

Published on 04 Jun 2019 - 14:39

score 279 · Answer 7 · 2019-06-05 04:34:04

279

Views

Proof that a graph has lebesgue measure zero using fubini's thm

Published on 05 Jun 2019 - 4:34

score 216 · Answer 8 · 2019-06-05 20:46:18

216

Views

Lebesgue's Dominated Convergence Theorem $(g-f)$ is finite, is well defined?

Published on 05 Jun 2019 - 20:46

score 336 · Answer 9 · 2019-06-06 03:19:26

336

Views

Interchange of Integral and partial derivative in Measure Theory

Published on 06 Jun 2019 - 3:19

score 280 · Answer 10 · 2026-03-25 04:57:29

280

Views

Measure of a cone

Published on 25 Mar 2026 - 4:57

score 83 · Answer 11 · 2026-03-25 20:11:59

83

Views

If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.

Published on 25 Mar 2026 - 20:11

score 186 · Answer 12 · 2026-03-22 07:19:50

186

Views

Is $f(x,y)=\operatorname{sgn}(x-y)e^{-|x-y|}$ Lebesgue integrable?

Published on 22 Mar 2026 - 7:19

score 48 · Answer 13 · 2019-06-09 02:19:18

48

Views

Showing that $f(x)x^{-3/2}$ is integrable on $[0,1]$ with $f$ continous, $f(0)=0$ and $f'(0)$ exists.

Published on 09 Jun 2019 - 2:19

score 67 · Answer 14 · 2019-06-09 04:43:13

67

Views

Limit of Integral of $L^1$ function times $\frac{x}{n}$

Published on 09 Jun 2019 - 4:43

score 45 · Answer 15 · 2019-06-11 09:16:09

45

Views

Convergence of convolution with a function which has Cesaro average

Published on 11 Jun 2019 - 9:16

List Question

If f is a measurable function with $\int_{[0,1]}(f(x))^{2} dm(x) < \infty$ then $\int_{[0,1]}|f(x)| dm(x) < \infty$.

Integral of bounded measurable function with convergent sequence of measures.

If $f$ is integrable, does $\int f = \lim \int f_n$ hold?

Calculating $ \lim_{n \rightarrow \infty} \int_{[0, \infty)} \frac{\sin(e^x) }{1+nx^2}\,dx$

Calculating $ \lim_{n \rightarrow \infty} \int_{[1, \infty)} \frac{n \sin(\frac{x}{n}) }{x^3}\,dx$

How to calculate an integral given a measure?

Proof that a graph has lebesgue measure zero using fubini's thm

Lebesgue's Dominated Convergence Theorem $(g-f)$ is finite, is well defined?

Interchange of Integral and partial derivative in Measure Theory

Measure of a cone

If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.

Is $f(x,y)=\operatorname{sgn}(x-y)e^{-|x-y|}$ Lebesgue integrable?

Showing that $f(x)x^{-3/2}$ is integrable on $[0,1]$ with $f$ continous, $f(0)=0$ and $f'(0)$ exists.

Limit of Integral of $L^1$ function times $\frac{x}{n}$

Convergence of convolution with a function which has Cesaro average

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