Please, I need a small help with a reference.


Lets say we do have a continuous functional $f$ on $L^1$ space and we want to prove the existence of extremals $f(\Omega)$, where $\Omega$ is compact and bounded.


I have heard, that the generalized cantor's theorem is the way to prove the existence, but I am unfortunately unable to find the proof, or the theorem itself (other than the set theory with $2^A$ $2^{2^A}$...).


Do You know about any reference, that would supply me with the proof?


Thank You very much!



Extremal of an L^1 continuous functional on a compact bounded set
Found it out.


There might have been a mistake, the proof should not be Cantors generalized theorem, but just a generalization of the basic fact, that a continuous function on a compact closed set attains extremas.


