Separability of $ L_p $ spaces I would like to know if the Lebesgue spaces $L_p$ with $ 0 < p < 1 $ are separable or not.
I know that this is true for $1 \leq p < + \infty$, but I do not find any references for the 
case  $ 0 < p < 1 $.
Thank you 

Please refer this article. It talks about $L_{p}$ spaces for $0 < p \leq 1$. Link: 
http://www.jstor.org/stable/2041603?seq=2
Look at the step functions, the ones that take rational values  and whose steps have rational endpoints there should be only countably many of those. And then you can perhaps apply the same argument, you use to prove it for $L_{p}$ spaces for $1 < p < \infty$.
