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A good book of functional analysis

This is an old post, but I still want to give some personal recommendations. In “study order”, so to speak, and with the aim of keeping the number of texts to be digested small, my list is: G. ...
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Does some published texbook take a particular approach (described here) to the transition from discrete to continuous probability distributions?

Such a transition from the discrete to the continuous is precisely the point of Nelson's Radically Elementary Probability Theory (REPT). It recently turned out that when viewed as a subsystem of BST,...
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