Question

Rudin, Riesz Representation Step X: Why do we need $|a|$?

score 196 · Answer 1 · 2026-03-25 17:37:08

196

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Rudin, Riesz Representation Step X: Why do we need $|a|$?

Published on 25 Mar 2026 - 17:37

score 53 · Answer 2 · 2020-04-19 00:56:54

53

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Let $f_n \to f$ in $L^1[0,1]$, prove $\int_{0}^{1}e^f\leq \liminf _{n \to \infty}\int_{0}^{1}e^{f_n}$

Published on 19 Apr 2020 - 0:56

score 120 · Answer 3 · 2026-04-01 15:43:37

120

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Is the linear extension of the inverse Fourier transform "equal to" the inverse Fourier-Plancherel transform?

Published on 01 Apr 2026 - 15:43

score 44 · Answer 4 · 2020-04-19 06:23:03

44

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$ \left( f_k:x \mapsto \chi_k(x) \left(1-\frac{x}{k}\right)^k e^{x/2} \right)_k$ is increasing; [monotone convergence theorem]

Published on 19 Apr 2020 - 6:23

score 48 · Answer 5 · 2020-04-19 17:08:27

48

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Riemann and Lebesgue Integral, a simple question.

Published on 19 Apr 2020 - 17:08

score 27 · Answer 6 · 2020-04-19 19:42:41

27

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If $f_n \rightharpoonup f$ in $L^2[0,1]$, then $F_n\to F$ uniformly where $F_n=\int_{0}^{x}f_n$

Published on 19 Apr 2020 - 19:42

score 59 · Answer 7 · 2020-04-19 22:21:37

59

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Let $f,g \in L^2$, find the limit $\lim_{t \to \infty}\frac{\|f+tg\|_2-\|f\|_2}{t}$

Published on 19 Apr 2020 - 22:21

score 614 · Answer 8 · 2026-03-28 05:20:41

614

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Subharmonic functions and monotonically increasing integrals

Published on 28 Mar 2026 - 5:20

score 27 · Answer 9 · 2020-04-20 19:59:32

27

Views

Finding a convergent subsequence in $L^1(\mathbb{R})$ using a Fubini argument

Published on 20 Apr 2020 - 19:59

score 95 · Answer 10 · 2020-04-20 22:25:08

95

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Let $f,f' \in L^1$, show $\int_\mathbb{R} f'=0$

Published on 20 Apr 2020 - 22:25

score 73 · Answer 11 · 2020-04-21 14:39:42

73

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Lebesgue Dominated Convergence Theorem for integral of $\sin$

Published on 21 Apr 2020 - 14:39

score 460 · Answer 12 · 2020-04-21 14:54:03

460

Views

Show that $f = 0$ almost everywhere

Published on 21 Apr 2020 - 14:54

score 24 · Answer 13 · 2020-04-21 15:40:23

24

Views

Measurable and Lebesgue Integral function

Published on 21 Apr 2020 - 15:40

score 59 · Answer 14 · 2020-04-22 01:21:16

59

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Why is this set measurable?

Published on 22 Apr 2020 - 1:21

score 75 · Answer 15 · 2020-04-22 16:46:49

75

Views

Let $f\geq0$ and that $\int_{0}^{x}f(t)dt<e^x$ for all $0\leq x$, show $f(t)e^{-at}\in L^1[0,\infty)$, $a>1$

Published on 22 Apr 2020 - 16:46

List Question

Rudin, Riesz Representation Step X: Why do we need $|a|$?

Let $f_n \to f$ in $L^1[0,1]$, prove $\int_{0}^{1}e^f\leq \liminf _{n \to \infty}\int_{0}^{1}e^{f_n}$

Is the linear extension of the inverse Fourier transform "equal to" the inverse Fourier-Plancherel transform?

$ \left( f_k:x \mapsto \chi_k(x) \left(1-\frac{x}{k}\right)^k e^{x/2} \right)_k$ is increasing; [monotone convergence theorem]

Riemann and Lebesgue Integral, a simple question.

If $f_n \rightharpoonup f$ in $L^2[0,1]$, then $F_n\to F$ uniformly where $F_n=\int_{0}^{x}f_n$

Let $f,g \in L^2$, find the limit $\lim_{t \to \infty}\frac{\|f+tg\|_2-\|f\|_2}{t}$

Subharmonic functions and monotonically increasing integrals

Finding a convergent subsequence in $L^1(\mathbb{R})$ using a Fubini argument

Let $f,f' \in L^1$, show $\int_\mathbb{R} f'=0$

Lebesgue Dominated Convergence Theorem for integral of $\sin$

Show that $f = 0$ almost everywhere

Measurable and Lebesgue Integral function

Why is this set measurable?

Let $f\geq0$ and that $\int_{0}^{x}f(t)dt<e^x$ for all $0\leq x$, show $f(t)e^{-at}\in L^1[0,\infty)$, $a>1$

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