Question

MCT, DCT, and Fatou's Lemma related problems Bank

score 107 · Answer 1 · 2019-10-26 10:38:43

107

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MCT, DCT, and Fatou's Lemma related problems Bank

Published on 26 Oct 2019 - 10:38

score 130 · Answer 2 · 2019-10-26 12:55:54

130

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Why it's not true that $\frac{d}{dt}\int f(t,x)dx=\int \frac{\partial }{\partial t}f(t,x)dx$ where $f(t,x)=g(x)sign(t-x)$?

Published on 26 Oct 2019 - 12:55

score 449 · Answer 3 · 2019-10-26 19:21:53

449

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Let $f\in L^p$ and $g\in L^q$, then $f=0$ iff $\int fg=0$ for all $g$

Published on 26 Oct 2019 - 19:21

score 130 · Answer 4 · 2019-10-26 19:34:56

130

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Finding $\lim_{n\to \infty}\int_{(0,\infty)}\frac{dt}{\left(1+\frac{t}{n}\right)^nt^{1/n}}$

Published on 26 Oct 2019 - 19:34

score 50 · Answer 5 · 2019-10-27 14:27:37

50

Views

Prove that $\frac{d}{dy}\int\limits_{0}^1f(x,y)dm(x)=\int\limits_0^1\frac{df}{dy}dm(x)$

Published on 27 Oct 2019 - 14:27

score 46 · Answer 6 · 2019-10-28 10:00:28

46

Views

Proving proposition 23 in case of $f < 0$ on pg.92 & 93 in "Royden and Fitzpatrick".

Published on 28 Oct 2019 - 10:00

score 564 · Answer 7 · 2026-02-23 06:39:32

564

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Lebesgue integral and change of measure

Published on 23 Feb 2026 - 6:39

score 820 · Answer 8 · 2019-10-28 15:08:39

820

Views

Using dominated convergence theorem with "continuous" limits

Published on 28 Oct 2019 - 15:08

score 59 · Answer 9 · 2019-10-28 19:49:56

59

Views

Question about lesbesgue functions

Published on 28 Oct 2019 - 19:49

score 42 · Answer 10 · 2019-10-29 02:08:08

42

Views

If $f_n \to f$ in $L^1$ and $\chi_Af_n,\chi_Af \in L^1$ does $\chi_Af_n \to \chi_Af$ in $L^1$?

Published on 29 Oct 2019 - 2:08

score 50 · Answer 11 · 2019-10-29 03:14:53

50

Views

Am I applying the Dominated Convergence Test correctly in this example?

Published on 29 Oct 2019 - 3:14

score 1.2k · Answer 12 · 2019-10-29 06:47:06

1.2k

Views

Lebesgue measure of closed interval

Published on 29 Oct 2019 - 6:47

score 50 · Answer 13 · 2019-10-29 17:41:34

50

Views

On the $w^{\ast}$ Convergence of a Sequence of Measures

Published on 29 Oct 2019 - 17:41

score 320 · Answer 14 · 2019-10-29 18:16:25

320

Views

Lebesgue integrable sin(1/x)

Published on 29 Oct 2019 - 18:16

score 130 · Answer 15 · 2019-10-29 23:26:52

130

Views

$\forall \epsilon>0 , \exists$ a finite linear combination of charactristic functions of intervals such that $\|f-\phi\|_{L^1}<\epsilon$.

Published on 29 Oct 2019 - 23:26

List Question

MCT, DCT, and Fatou's Lemma related problems Bank

Why it's not true that $\frac{d}{dt}\int f(t,x)dx=\int \frac{\partial }{\partial t}f(t,x)dx$ where $f(t,x)=g(x)sign(t-x)$?

Let $f\in L^p$ and $g\in L^q$, then $f=0$ iff $\int fg=0$ for all $g$

Finding $\lim_{n\to \infty}\int_{(0,\infty)}\frac{dt}{\left(1+\frac{t}{n}\right)^nt^{1/n}}$

Prove that $\frac{d}{dy}\int\limits_{0}^1f(x,y)dm(x)=\int\limits_0^1\frac{df}{dy}dm(x)$

Proving proposition 23 in case of $f < 0$ on pg.92 & 93 in "Royden and Fitzpatrick".

Lebesgue integral and change of measure

Using dominated convergence theorem with "continuous" limits

Question about lesbesgue functions

If $f_n \to f$ in $L^1$ and $\chi_Af_n,\chi_Af \in L^1$ does $\chi_Af_n \to \chi_Af$ in $L^1$?

Am I applying the Dominated Convergence Test correctly in this example?

Lebesgue measure of closed interval

On the $w^{\ast}$ Convergence of a Sequence of Measures

Lebesgue integrable sin(1/x)

$\forall \epsilon>0 , \exists$ a finite linear combination of charactristic functions of intervals such that $\|f-\phi\|_{L^1}<\epsilon$.

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