Question

Is $L^p$ for $0<p<1$ quasi-normed?

score 574 · Answer 1 · 2026-04-16 01:28:01

574

Views

Is $L^p$ for $0<p<1$ quasi-normed?

Published on 16 Apr 2026 - 1:28

score 109 · Answer 2 · 2026-04-16 06:59:23

109

Views

If $f(t)$ fulfill $\int_{-\infty}^\infty |f(t)|dt < \infty$, Is then true $\int_{-\infty}^\infty |f(t)|^2 dt < \infty$? If not, What else is needed?

Published on 16 Apr 2026 - 6:59

score 43 · Answer 3 · 2026-04-15 21:31:53

43

Views

Determine the cases, $L^0\left(\lambda\right)$ and $L^\infty\left(\lambda\right)$

Published on 15 Apr 2026 - 21:31

score 44 · Answer 4 · 2026-04-12 03:28:51

44

Views

Can anyone give an example of a relatively compact set in $\ell_p$ which is not majorable?

Published on 12 Apr 2026 - 3:28

score 62 · Answer 5 · 2026-04-16 17:41:57

62

Views

Why can you not switch the limits of $\lim_{n\rightarrow\infty}\lim_{p\rightarrow\infty}||\textbf{1}_{A_n}f||_p$?

Published on 16 Apr 2026 - 17:41

score 265 · Answer 6 · 2026-04-13 02:35:24

265

Views

Fréchet Derivative of a functional in $L^2$

Published on 13 Apr 2026 - 2:35

score 38 · Answer 7 · 2026-04-12 22:56:11

38

Views

Show that if some multiplication of functions is equal to 0 then the function is the zero function (a.e.)

Published on 12 Apr 2026 - 22:56

score 45 · Answer 8 · 2026-04-13 00:32:24

45

Views

Is it true that measurable functions that differ only in a null measure set are in the same class?

Published on 13 Apr 2026 - 0:32

score 153 · Answer 9 · 2026-04-13 15:00:26

153

Views

Largest and smallest norm on a vector space given a Hamel basis should be normalised in that norm

Published on 13 Apr 2026 - 15:00

score 35 · Answer 10 · 2026-04-15 05:01:15

35

Views

Does there exists any non-zero bounded function which satisfies Mean Value Property on $\Bbb{R}^n$?

Published on 15 Apr 2026 - 5:01

score 117 · Answer 11 · 2026-05-10 19:47:36

117

Views

Dual of a order continuous Banach Lattice $\subseteq L^1$

Published on 10 May 2026 - 19:47

score 113 · Answer 12 · 2026-04-13 13:16:49

113

Views

Existence of minimum of a functional on $L^p (0,1)$

Published on 13 Apr 2026 - 13:16

score 141 · Answer 13 · 2026-05-14 08:50:29

141

Views

$\dot{H}^1\subset L^6 $

Published on 14 May 2026 - 8:50

score 24 · Answer 14 · 2026-04-17 15:18:05

24

Views

For some probability measures $p$ and $q$, under what conditions do we have $L^2(p) \subseteq L^2(q)$?

Published on 17 Apr 2026 - 15:18

score 34 · Answer 15 · 2026-04-11 06:50:21

34

Views

Compact operators on $\ell^p$

Published on 11 Apr 2026 - 6:50

List Question

Is $L^p$ for $0<p<1$ quasi-normed?

If $f(t)$ fulfill $\int_{-\infty}^\infty |f(t)|dt < \infty$, Is then true $\int_{-\infty}^\infty |f(t)|^2 dt < \infty$? If not, What else is needed?

Determine the cases, $L^0\left(\lambda\right)$ and $L^\infty\left(\lambda\right)$

Can anyone give an example of a relatively compact set in $\ell_p$ which is not majorable?

Why can you not switch the limits of $\lim_{n\rightarrow\infty}\lim_{p\rightarrow\infty}||\textbf{1}_{A_n}f||_p$?

Fréchet Derivative of a functional in $L^2$

Show that if some multiplication of functions is equal to 0 then the function is the zero function (a.e.)

Is it true that measurable functions that differ only in a null measure set are in the same class?

Largest and smallest norm on a vector space given a Hamel basis should be normalised in that norm

Does there exists any non-zero bounded function which satisfies Mean Value Property on $\Bbb{R}^n$?

Dual of a order continuous Banach Lattice $\subseteq L^1$

Existence of minimum of a functional on $L^p (0,1)$

$\dot{H}^1\subset L^6 $

For some probability measures $p$ and $q$, under what conditions do we have $L^2(p) \subseteq L^2(q)$?

Compact operators on $\ell^p$

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