Question

Prove that the piecewise function $f$ is integrable

score 42 · Answer 1 · 2026-04-13 16:01:53

42

Views

Prove that the piecewise function $f$ is integrable

Published on 13 Apr 2026 - 16:01

score 55 · Answer 2 · 2026-04-13 02:26:41

55

Views

Verifying the countably additive measure property of $\nu_f$ when $\nu_f(E)$ is infinite

Published on 13 Apr 2026 - 2:26

score 49 · Answer 3 · 2023-11-15 09:58:57

49

Views

Calculate $\displaystyle\lim_{n\to\infty} \int_R \frac{1+nx}{(1+x)^n } 1_{[0,1]} (x) d\lambda$

Published on 15 Nov 2023 - 9:58

score 40 · Answer 4 · 2023-11-15 12:00:40

40

Views

$f_n=\frac{2+(-1)^n}{n}1_{[0,n]} (x) $ and usage of Lemma of Fatou

Published on 15 Nov 2023 - 12:00

score 47 · Answer 5 · 2026-04-13 09:36:50

47

Views

Area under the graph is not the integral when the measure is not $\sigma$-finite?

Published on 13 Apr 2026 - 9:36

score 62 · Answer 6 · 2023-11-17 21:03:47

62

Views

Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

Published on 17 Nov 2023 - 21:03

score 60 · Answer 7 · 2023-11-19 01:49:55

60

Views

If $m(A)=0$, does this imply that $m(\log(A)) = 0$ when $A\subset \mathbb{R}_{+}$

Published on 19 Nov 2023 - 1:49

score 48 · Answer 8 · 2026-04-10 23:35:45

48

Views

$n-$ forms and relation to Lebesgue integral

Published on 10 Apr 2026 - 23:35

score 32 · Answer 9 · 2023-11-20 15:25:33

32

Views

Check lebesgue integrable or not...

Published on 20 Nov 2023 - 15:25

score 62 · Answer 10 · 2026-04-07 18:11:14

62

Views

How to compare $L^p$ norm in the interior with the $L^p$ norm at the boundary?

Published on 07 Apr 2026 - 18:11

score 49 · Answer 11 · 2026-04-09 23:33:09

49

Views

Properties of Lebesgue points of a function

Published on 09 Apr 2026 - 23:33

score 30 · Answer 12 · 2026-04-11 11:20:26

30

Views

Maximization-integral interchange rules

Published on 11 Apr 2026 - 11:20

score 81 · Answer 13 · 2023-11-22 15:09:53

81

Views

$\lim _{j \rightarrow \infty} \int|| f_j|-| f|-| f_j-f \|=0$

Published on 22 Nov 2023 - 15:09

score 56 · Answer 14 · 2026-04-13 09:39:43

56

Views

Proof of $|x|^{-\alpha} \in W^{1,p}(U)$

Published on 13 Apr 2026 - 9:39

score 61 · Answer 15 · 2023-11-23 14:56:49

$\lim_{n\to\infty} ||f_n-f||_p=0 $ prove that for every $\epsilon>0$ there exists a $\delta$ with $\mu(A)<\delta $-> $\int_A|f_n|^p d\mu <\epsilon$

List Question

Prove that the piecewise function $f$ is integrable

Verifying the countably additive measure property of $\nu_f$ when $\nu_f(E)$ is infinite

Calculate $\displaystyle\lim_{n\to\infty} \int_R \frac{1+nx}{(1+x)^n } 1_{[0,1]} (x) d\lambda$

$f_n=\frac{2+(-1)^n}{n}1_{[0,n]} (x) $ and usage of Lemma of Fatou

Area under the graph is not the integral when the measure is not $\sigma$-finite?

Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

If $m(A)=0$, does this imply that $m(\log(A)) = 0$ when $A\subset \mathbb{R}_{+}$

$n-$ forms and relation to Lebesgue integral

Check lebesgue integrable or not...

How to compare $L^p$ norm in the interior with the $L^p$ norm at the boundary?

Properties of Lebesgue points of a function

Maximization-integral interchange rules

$\lim _{j \rightarrow \infty} \int|| f_j|-| f|-| f_j-f \|=0$

Proof of $|x|^{-\alpha} \in W^{1,p}(U)$

$\lim_{n\to\infty} ||f_n-f||_p=0 $ prove that for every $\epsilon>0$ there exists a $\delta$ with $\mu(A)<\delta $-> $\int_A|f_n|^p d\mu <\epsilon$

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