What does $L^2$(R) mean?

Question

I am reading about wavelets and it mentions something about "a function in $L^2(\mathbb{R})$". What does that even mean?

It means square-integrable. See https://en.wikipedia.org/wiki/Lp_space — anon, Aug 11 '15 at 21:43
It means the functional space with elements integral of square over the entire real numbers of which is finite. $f \in L^2 (\mathbb R): \int_{-\infty}^{+\infty}f^2 dx < M$. — Kaster, Aug 11 '15 at 21:44
@Kaster $\int_{-\infty}^\infty f^2 dx < + \infty$ is more precise. — Zhanxiong, Aug 11 '15 at 21:46
It means you probably need to learn some real analysis (measure theory and a little bit of Fourier analysis) before trying to learn about wavelets... — David C. Ullrich, Aug 11 '15 at 22:18
The $L$ stands for Lebesgue, and $\Bbb R$ denotes the real numbers. If you aren't even familiar with the notation $\Bbb R$, then I second Ulrich that you need to learn some basics first. — anon, Aug 11 '15 at 23:10
I did do fourier analysis in my MEng Electronic Engineering degree so I am familiar with R and Z and other things. But I am not sure about L and was not sure if this R is the R I think it is. — quantum231, Aug 12 '15 at 17:23

score 7 · Accepted Answer · answered Aug 11 '15 at 21:43

7

$L^2(R)$ likely denotes the space of square-integrable functions on $R$.

answered Aug 11 '15 at 21:43

Dan

1 Answers1