Question

Proving that $\displaystyle\int_0^\infty f(t)\frac{\sin(xt)}{t}dt$ exist for $f\in\mathcal{L}^p(0,\infty)$, $1<p<\infty$ and $x>0$

score 49 · Answer 1 · 2026-04-30 05:05:17

49

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Proving that $\displaystyle\int_0^\infty f(t)\frac{\sin(xt)}{t}dt$ exist for $f\in\mathcal{L}^p(0,\infty)$, $1<p<\infty$ and $x>0$

Published on 30 Apr 2026 - 5:05

score 159 · Answer 2 · 2026-04-09 10:43:35

159

Views

counting measure I need help

Published on 09 Apr 2026 - 10:43

score 930 · Answer 3 · 2026-04-16 09:16:33

930

Views

Continuity of convolution $f\ast g$ for $f\in C_0(\mathbb{R})$ and $g\in L^1(\mathbb{R})$.

Published on 16 Apr 2026 - 9:16

score 79 · Answer 4 · 2026-04-11 18:56:35

79

Views

Proving a function is identically $0$ using the fundamental theorem of calculus of variations

Published on 11 Apr 2026 - 18:56

score 58 · Answer 5 · 2026-04-16 01:52:02

58

Views

Show that: $ \int_{[a,b]} \liminf_{n\rightarrow \infty} f_n(x) d\lambda(x)\le \lim_{\varepsilon\searrow0}(f(b-\varepsilon)-f(a+\varepsilon)) $

Published on 16 Apr 2026 - 1:52

score 126 · Answer 6 · 2026-04-15 14:58:33

126

Views

Inequality of $L^p \left ( \mathbb{R} \right )$ norms of functions and their derivatives

Published on 15 Apr 2026 - 14:58

score 210 · Answer 7 · 2026-04-11 09:27:46

210

Views

Advantages of Lebesgue measurable sets over Borel ones in $L^p$ theory?

Published on 11 Apr 2026 - 9:27

score 7.1k · Answer 8 · 2026-04-23 19:58:36

7.1k

Views

Expectation of Random variable times indicator function of zero probability event is equal zero

Published on 23 Apr 2026 - 19:58

score 90 · Answer 9 · 2026-04-13 12:34:04

90

Views

Divergence of a particular integral

Published on 13 Apr 2026 - 12:34

score 147 · Answer 10 · 2026-04-12 11:39:14

147

Views

Problems with Fubinis theorem

Published on 12 Apr 2026 - 11:39

score 354 · Answer 11 · 2026-04-11 21:51:05

354

Views

Lebesgue integral over Cantor set, would like confirmation of my solution.

Published on 11 Apr 2026 - 21:51

score 125 · Answer 12 · 2026-04-11 08:08:11

125

Views

How should this limit superior from a proof of the Lebesgue Differentiation Theorem be interpreted?

Published on 11 Apr 2026 - 8:08

score 50 · Answer 13 · 2026-04-14 06:17:32

50

Views

Does this converge to $\int f \phi '$?

Published on 14 Apr 2026 - 6:17

score 1.8k · Answer 14 · 2026-04-12 14:33:28

1.8k

Views

Can you Lebesgue integrate a complex function on a curve?

Published on 12 Apr 2026 - 14:33

score 51 · Answer 15 · 2026-04-12 18:03:53

51

Views

lebesgue measurable limit

Published on 12 Apr 2026 - 18:03

List Question

Proving that $\displaystyle\int_0^\infty f(t)\frac{\sin(xt)}{t}dt$ exist for $f\in\mathcal{L}^p(0,\infty)$, $1<p<\infty$ and $x>0$

counting measure I need help

Continuity of convolution $f\ast g$ for $f\in C_0(\mathbb{R})$ and $g\in L^1(\mathbb{R})$.

Proving a function is identically $0$ using the fundamental theorem of calculus of variations

Show that: $ \int_{[a,b]} \liminf_{n\rightarrow \infty} f_n(x) d\lambda(x)\le \lim_{\varepsilon\searrow0}(f(b-\varepsilon)-f(a+\varepsilon)) $

Inequality of $L^p \left ( \mathbb{R} \right )$ norms of functions and their derivatives

Advantages of Lebesgue measurable sets over Borel ones in $L^p$ theory?

Expectation of Random variable times indicator function of zero probability event is equal zero

Divergence of a particular integral

Problems with Fubinis theorem

Lebesgue integral over Cantor set, would like confirmation of my solution.

How should this limit superior from a proof of the Lebesgue Differentiation Theorem be interpreted?

Does this converge to $\int f \phi '$?

Can you Lebesgue integrate a complex function on a curve?

lebesgue measurable limit

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