Jan 20, 2015 · L0 norm, L1 norm and L2 norm Ask Question Asked 10 years, 10 months ago Modified 7 years, 8 months ago

This definition of the "0-norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) $0^ {0}$ is conventionally defined to be 1.

it's defined in the Wikipedia article (not as a norm, which is why I used quotes). The Wikipedia article defines the topology induced by the "norm," which is convergence in measure.

Jul 8, 2014 · The $L_0$ norm of $x$ is $\sum\limits_k x_k^0$, in a similar manner to $L_p$ norms for $p \ge 1$, but avoiding the problem of dividing by zero that would come from ...

May 24, 2021 · I will take note of the notation next time. Thanks for the suggestion. But what if $\mu$ is defined to be an atomless probability measure? I do think the argument holds.

For $0 < p < \\infty$, the definitions of the spaces $L^p$ are very natural. Then, we of course want $L^\\infty$ and $L^0$ to be some kind of limits of $L^p ...

May 16, 2013 · A lot of papers refer to it as a "pseudo-norm" or "quasi-norm" but they do not mean this in the standard mathematical sense, they just mean it is not a norm, and are being loose with …

Feb 6, 2021 · I am not a mathematics student but somehow have to know about L1 and L2 norms. I am looking for some appropriate sources to learn these things and know they work and what are their …

Jul 19, 2021 · I have a quite clear idea of the definition of $L^p (\Omega, \mathcal {F}, P)$ spaces, for $0 < p \leq \infty$. But, I don't understand the definition (from the ...

Jun 21, 2013 · I have seen the claim that the l0-norm ($\|X\|_0$ = support (X)) is a pseudo-norm because it does not satisfy all properties of a norm. I thought it to be triangle inequality, but am not …