Question

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

score 39 · Answer 1 · 2026-03-29 14:59:23

39

Views

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

Published on 29 Mar 2026 - 14:59

score 159 · Answer 2 · 2019-12-02 05:51:45

159

Views

Separability L_p spaces without $\sigma$-finiteness

Published on 02 Dec 2019 - 5:51

score 62 · Answer 3 · 2019-12-02 11:48:49

62

Views

For which $p\ge 1$ is a function an element of an $L^p$ space?

Published on 02 Dec 2019 - 11:48

score 121 · Answer 4 · 2026-04-02 05:30:33

121

Views

Do we have $f(x)\le\limsup x_n$ for every functional extending limit?

Published on 02 Apr 2026 - 5:30

score 33 · Answer 5 · 2019-12-03 03:36:11

33

Views

$(f_{n})$ sequence of measurable functions in $L_{p},$ and $f_{n}\rightarrow f$ uniformly, $f=0$ a.e $\implies f\in L_{p}$

Published on 03 Dec 2019 - 3:36

score 69 · Answer 6 · 2019-12-03 08:07:09

69

Views

Likely-False Converse to Hölder Inequality

Published on 03 Dec 2019 - 8:07

score 381 · Answer 7 · 2026-04-02 03:33:23

381

Views

Local vs global Sobolev space

Published on 02 Apr 2026 - 3:33

score 32 · Answer 8 · 2019-12-03 22:16:01

32

Views

Why do we need $||f||_\infty > 0$ to show $||f||_\infty = \sup\{a : \mu(\{x : |f(x)| > a\}) > 0\}$?

Published on 03 Dec 2019 - 22:16

score 491 · Answer 9 · 2026-03-27 02:35:58

491

Views

Derivative $L^p$-$L^q$ Estimates of linear heat equation

Published on 27 Mar 2026 - 2:35

score 54 · Answer 10 · 2019-12-04 16:32:25

54

Views

Convergence of conditional expectation of a function

Published on 04 Dec 2019 - 16:32

score 338 · Answer 11 · 2019-12-04 23:10:02

338

Views

Every $f\in L_{1}$ can be approximated by simple functions.

Published on 04 Dec 2019 - 23:10

score 33 · Answer 12 · 2019-12-05 05:21:07

33

Views

$ T(g)=0$ for all $g\in L^2\cap L^1$ implies $T(g)=0$ for all $g\in L^2\cap L^p$?

Published on 05 Dec 2019 - 5:21

score 179 · Answer 13 · 2019-12-05 20:48:07

179

Views

Example of a function which is not in $L^p$ for $p\neq 2, 0<p<\infty$

Published on 05 Dec 2019 - 20:48

score 187 · Answer 14 · 2019-12-06 09:53:55

187

Views

What is the operator norm of the left shift operator $T_t:\phi(x) \mapsto \phi(x+t)$ in $L^2(\mathbb{R},e^{-x^2}dx)$?

Published on 06 Dec 2019 - 9:53

score 96 · Answer 15 · 2019-12-06 20:09:13

96

Views

Cauchy-Schwarz-like inequality for a self-adjoint nonnegativity-preserving operator on $L^2$

Published on 06 Dec 2019 - 20:09

List Question

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

Separability L_p spaces without $\sigma$-finiteness

For which $p\ge 1$ is a function an element of an $L^p$ space?

Do we have $f(x)\le\limsup x_n$ for every functional extending limit?

$(f_{n})$ sequence of measurable functions in $L_{p},$ and $f_{n}\rightarrow f$ uniformly, $f=0$ a.e $\implies f\in L_{p}$

Likely-False Converse to Hölder Inequality

Local vs global Sobolev space

Why do we need $||f||_\infty > 0$ to show $||f||_\infty = \sup\{a : \mu(\{x : |f(x)| > a\}) > 0\}$?

Derivative $L^p$-$L^q$ Estimates of linear heat equation

Convergence of conditional expectation of a function

Every $f\in L_{1}$ can be approximated by simple functions.

$ T(g)=0$ for all $g\in L^2\cap L^1$ implies $T(g)=0$ for all $g\in L^2\cap L^p$?

Example of a function which is not in $L^p$ for $p\neq 2, 0<p<\infty$

What is the operator norm of the left shift operator $T_t:\phi(x) \mapsto \phi(x+t)$ in $L^2(\mathbb{R},e^{-x^2}dx)$?

Cauchy-Schwarz-like inequality for a self-adjoint nonnegativity-preserving operator on $L^2$

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