Most of elegant results in stochastic processes are from two underlying structures: Markovian and Martingale . The reason would be that those are fairly strong assumptions , and just a step away from random walks .
One perspective to see w hy the Hahn-Banach theorem is considered as the first big theorem in linear functional analysis. The geometric version of the Hahn-Banach theorem is the hyperplane separation theorem (geometrically, the theorem is so obv ...
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