All Questions

Working over ZF but without the Axiom of Choice (AC), assume that the Hahn–Banach Theorem holds for $\ell^\infty$. Does it follow that there exists a set of real numbers that is not Lebesgue ...

There is a classical theorem of Riesz-Kolmogorov that characterizes compact embedding in $L^p$-spaces of some subspace of them. A generalization to arbitrary metric spaces has been recently obtained ...

I am trying to prove this theorem. I have not found anything similar to it on the internet. Special version of Tonelli’s theorem Assume that the functions $f(x,u): [a,b] \times \mathbb{R} \to \mathbb{...