Question

If $\mu(|f_n|^p)$ is bounded and $f_n\to f$ in measure then $f_n\to f$ in $L^1$

score 254 · Answer 1 · 2026-04-16 10:42:41

254

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If $\mu(|f_n|^p)$ is bounded and $f_n\to f$ in measure then $f_n\to f$ in $L^1$

Published on 16 Apr 2026 - 10:42

score 367 · Answer 2 · 2026-04-14 07:23:17

367

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Showing continuous functions are dense in $L^p([0,1],\lambda)$, where $\lambda$ is Lebesgue measure

Published on 14 Apr 2026 - 7:23

score 475 · Answer 3 · 2026-04-13 04:58:39

475

Views

The density of polynomials in the space of continuous functions on the unit ball of $\ell^p$

Published on 13 Apr 2026 - 4:58

score 1.2k · Answer 4 · 2026-04-11 05:21:50

1.2k

Views

"Scalar product" of two Lp spaces

Published on 11 Apr 2026 - 5:21

score 474 · Answer 5 · 2026-04-09 02:30:17

474

Views

Volterra-like operator is bounded

Published on 09 Apr 2026 - 2:30

score 745 · Answer 6 · 2026-04-17 07:00:42

745

Views

$1 \le p < q < \infty$ implies $L^q \subset L^p$

Published on 17 Apr 2026 - 7:00

score 49 · Answer 7 · 2026-04-11 06:06:30

49

Views

What powers of $|x|$ belong to $L^1$?

Published on 11 Apr 2026 - 6:06

score 65 · Answer 8 · 2026-04-17 13:19:48

65

Views

If $\phi$ vanishes outside of $|x| < 2$, $\phi = 1$ where $|x| < 1$, prove/disprove $f * \phi$ is in $L^1$/$L^2$

Published on 17 Apr 2026 - 13:19

score 28 · Answer 9 · 2026-03-30 19:27:09

28

Views

Fractions in L^\infty

Published on 30 Mar 2026 - 19:27

score 51 · Answer 10 · 2026-04-14 22:55:04

51

Views

The convergence of a product of sequences converging in $L^2$.

Published on 14 Apr 2026 - 22:55

score 274 · Answer 11 · 2026-04-17 12:33:57

274

Views

Give an example of a linearly independent sequence $[x_0,x_1,x_2,\dots]$ of vectors in $\ell^{\infty}$ such that $\sum_{n=1}^{\infty} (x_n) =0$

Published on 17 Apr 2026 - 12:33

score 261 · Answer 12 · 2026-04-13 09:02:03

261

Views

Examples of Lp spaces in Applied Math

Published on 13 Apr 2026 - 9:02

score 450 · Answer 13 · 2026-04-12 14:32:37

450

Views

Is this subspace closed?(linear functions converges always to a linear function?)

Published on 12 Apr 2026 - 14:32

score 425 · Answer 14 · 2026-04-08 05:28:17

425

Views

Absolute moments Inequalities

Published on 08 Apr 2026 - 5:28

score 135 · Answer 15 · 2026-04-15 19:25:41

135

Views

$\displaystyle \lim_{p \to \infty} \lVert x \rVert _p = \lVert x \rVert _{\infty}$ is uniform in $x$?

Published on 15 Apr 2026 - 19:25

List Question

If $\mu(|f_n|^p)$ is bounded and $f_n\to f$ in measure then $f_n\to f$ in $L^1$

Showing continuous functions are dense in $L^p([0,1],\lambda)$, where $\lambda$ is Lebesgue measure

The density of polynomials in the space of continuous functions on the unit ball of $\ell^p$

"Scalar product" of two Lp spaces

Volterra-like operator is bounded

$1 \le p < q < \infty$ implies $L^q \subset L^p$

What powers of $|x|$ belong to $L^1$?

If $\phi$ vanishes outside of $|x| < 2$, $\phi = 1$ where $|x| < 1$, prove/disprove $f * \phi$ is in $L^1$/$L^2$

Fractions in L^\infty

The convergence of a product of sequences converging in $L^2$.

Give an example of a linearly independent sequence $[x_0,x_1,x_2,\dots]$ of vectors in $\ell^{\infty}$ such that $\sum_{n=1}^{\infty} (x_n) =0$

Examples of Lp spaces in Applied Math

Is this subspace closed?(linear functions converges always to a linear function?)

Absolute moments Inequalities

$\displaystyle \lim_{p \to \infty} \lVert x \rVert _p = \lVert x \rVert _{\infty}$ is uniform in $x$?

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