Question

$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?

score 84 · Answer 1 · 2016-09-24 15:56:52

84

Views

$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?

Published on 24 Sep 2016 - 15:56

score 903 · Answer 2 · 2016-09-24 16:20:39

903

Views

Exercise 8.U - Bartle's The Elements of Integration

Published on 24 Sep 2016 - 16:20

score 846 · Answer 3 · 2016-09-24 20:48:25

846

Views

Let $F$ be the set of all $x\in l_{\infty}$ such that $x_n = 0$ for all but finitely many n. Is $F$ open? closed? neither?

Published on 24 Sep 2016 - 20:48

score 47 · Answer 4 · 2026-04-02 16:58:59

47

Views

Show that for all $f$ and $g$ in $\mathbb{L}^1(E_n)$ that $f(\circ)g(x-\circ) \in \mathbb{L}^1(E_n)$

Published on 02 Apr 2026 - 16:58

score 957 · Answer 5 · 2026-03-25 19:10:58

957

Views

Show that the map $A : l^p \rightarrow l^q $ is a bounded linear map

Published on 25 Mar 2026 - 19:10

score 290 · Answer 6 · 2026-03-26 19:20:55

290

Views

Bounded variation functions with $\|f\|:=\|f\|_{L^1}+\|f'\|_{L^1}$: Banach space (after identifying any a.e. equal $f,g$)?

Published on 26 Mar 2026 - 19:20

score 59 · Answer 7 · 2016-10-02 12:16:04

59

Views

Does $\|f_j-f\|_p \rightarrow 0$ imply $\|f_j\|_p \rightarrow \|f\|_p$?

Published on 02 Oct 2016 - 12:16

score 37 · Answer 8 · 2016-10-05 07:01:07

37

Views

$\int_{\mathbb R} \left|\frac{1}{\sqrt{x_{n}}}f(y/x_{n})-g(y)\right|^2 dy \to 0 \implies f=0$

Published on 05 Oct 2016 - 7:01

score 235 · Answer 9 · 2026-04-02 16:59:26

235

Views

$L^\infty$ bound on smooth compactly supported function using Fourier transform

Published on 02 Apr 2026 - 16:59

score 314 · Answer 10 · 2016-10-08 21:16:08

314

Views

For which values $p, q$ does one have $L^{p} \subset L^{q}$?

Published on 08 Oct 2016 - 21:16

score 129 · Answer 11 · 2016-10-11 05:03:15

129

Views

metric space incomplete

Published on 11 Oct 2016 - 5:03

score 247 · Answer 12 · 2016-10-12 16:10:47

247

Views

Prove that if $1 \leq p \leq q \leq \infty$, then $||x||_q \leq ||x||_p$, for every $x \in\mathbb{R}^{n}$.

Published on 12 Oct 2016 - 16:10

score 62 · Answer 13 · 2016-10-13 10:33:03

62

Views

Is this true that the sequences evenly sampled from functions in $L^p$ are in $l_p$?

Published on 13 Oct 2016 - 10:33

score 31 · Answer 14 · 2016-10-14 01:07:46

31

Views

If a function produces closed sets in $\mathbb{R} ^{n}$ does it produce closed sets in subspaces of $\mathbb{R} ^{n}$?

Published on 14 Oct 2016 - 1:07

score 42 · Answer 15 · 2016-10-14 07:41:11

42

Views

Characterization of $L_{\mathrm{loc} }^p(\mathbb{R}^n)$ functions

Published on 14 Oct 2016 - 7:41

List Question

$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?

Exercise 8.U - Bartle's The Elements of Integration

Let $F$ be the set of all $x\in l_{\infty}$ such that $x_n = 0$ for all but finitely many n. Is $F$ open? closed? neither?

Show that for all $f$ and $g$ in $\mathbb{L}^1(E_n)$ that $f(\circ)g(x-\circ) \in \mathbb{L}^1(E_n)$

Show that the map $A : l^p \rightarrow l^q $ is a bounded linear map

Bounded variation functions with $\|f\|:=\|f\|_{L^1}+\|f'\|_{L^1}$: Banach space (after identifying any a.e. equal $f,g$)?

Does $\|f_j-f\|_p \rightarrow 0$ imply $\|f_j\|_p \rightarrow \|f\|_p$?

$\int_{\mathbb R} \left|\frac{1}{\sqrt{x_{n}}}f(y/x_{n})-g(y)\right|^2 dy \to 0 \implies f=0$

$L^\infty$ bound on smooth compactly supported function using Fourier transform

For which values $p, q$ does one have $L^{p} \subset L^{q}$?

metric space incomplete

Prove that if $1 \leq p \leq q \leq \infty$, then $||x||_q \leq ||x||_p$, for every $x \in\mathbb{R}^{n}$.

Is this true that the sequences evenly sampled from functions in $L^p$ are in $l_p$?

If a function produces closed sets in $\mathbb{R} ^{n}$ does it produce closed sets in subspaces of $\mathbb{R} ^{n}$?

Characterization of $L_{\mathrm{loc} }^p(\mathbb{R}^n)$ functions

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