Question

Integrable increasing function

score 67 · Answer 1 · 2018-06-14 10:40:52

67

Views

Integrable increasing function

Published on 14 Jun 2018 - 10:40

score 322 · Answer 2 · 2026-03-25 23:11:12

322

Views

Proving that a function related to the Fourier transform of the unit ball is in $L^1(\mathbb{R}^3)$

Published on 25 Mar 2026 - 23:11

score 69 · Answer 3 · 2018-06-15 08:23:51

69

Views

Lebesgue integrals

Published on 15 Jun 2018 - 8:23

score 468 · Answer 4 · 2018-06-16 22:15:16

468

Views

Caratheodory solutions of ODEs and sensitivity w.r.t. initial datum

Published on 16 Jun 2018 - 22:15

score 157 · Answer 5 · 2018-06-18 12:55:51

157

Views

How to prove $\sqrt{x}f(x) \to 0$?

Published on 18 Jun 2018 - 12:55

score 49 · Answer 6 · 2018-06-19 11:59:23

49

Views

If $\int_{[0,x]}f(t)\:\mathrm{d}t=0$ and $\int_{[x,0]}f(t)\:\mathrm{d}t=0$, $f=0$ almost everywhere.

Published on 19 Jun 2018 - 11:59

score 273 · Answer 7 · 2026-03-25 19:03:09

273

Views

An inequality with the characteristic function of a Distribution

Published on 25 Mar 2026 - 19:03

score 52 · Answer 8 · 2018-06-20 10:04:50

52

Views

Why does $\lim_{|x|\to\infty}|x|^n f(x)=0$ implies $f\in L^1(\mathbb{R}^n;\mathbb{C})$?

Published on 20 Jun 2018 - 10:04

score 60 · Answer 9 · 2018-06-20 13:52:41

60

Views

Definition of a positively integrable function

Published on 20 Jun 2018 - 13:52

score 70 · Answer 10 · 2018-06-21 01:08:04

70

Views

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

Published on 21 Jun 2018 - 1:08

score 82 · Answer 11 · 2018-06-21 09:11:05

82

Views

Decay of $C^2$-function where $f,f',f''$ are $\mathscr{L}^1$

Published on 21 Jun 2018 - 9:11

score 42 · Answer 12 · 2018-06-21 10:48:00

42

Views

Using measuretransformation

Published on 21 Jun 2018 - 10:48

score 59 · Answer 13 · 2018-06-22 11:09:45

59

Views

On the definition of integrability of simple functions

Published on 22 Jun 2018 - 11:09

score 225 · Answer 14 · 2026-02-22 23:12:15

225

Views

$f: [0,1] \to \mathbb{R}$ absolutely continuous, $f' \in \{0,1\}$ (a.e.), $f(0)=0$. Prove that for some measurable subset $A$, $f(x)=m(A \cap (0,x))$

Published on 22 Feb 2026 - 23:12

score 46 · Answer 15 · 2018-06-25 08:39:50

46

Views

In this proof, why does the space that has measure $0$ continue to increase?

Published on 25 Jun 2018 - 8:39

List Question

Integrable increasing function

Proving that a function related to the Fourier transform of the unit ball is in $L^1(\mathbb{R}^3)$

Lebesgue integrals

Caratheodory solutions of ODEs and sensitivity w.r.t. initial datum

How to prove $\sqrt{x}f(x) \to 0$?

If $\int_{[0,x]}f(t)\:\mathrm{d}t=0$ and $\int_{[x,0]}f(t)\:\mathrm{d}t=0$, $f=0$ almost everywhere.

An inequality with the characteristic function of a Distribution

Why does $\lim_{|x|\to\infty}|x|^n f(x)=0$ implies $f\in L^1(\mathbb{R}^n;\mathbb{C})$?

Definition of a positively integrable function

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

Decay of $C^2$-function where $f,f',f''$ are $\mathscr{L}^1$

Using measuretransformation

On the definition of integrability of simple functions

$f: [0,1] \to \mathbb{R}$ absolutely continuous, $f' \in \{0,1\}$ (a.e.), $f(0)=0$. Prove that for some measurable subset $A$, $f(x)=m(A \cap (0,x))$

In this proof, why does the space that has measure $0$ continue to increase?

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