Some Reminders of Functional Analysis
This short chapter is intended as an aide-mémoire of some fundamental results in functional analysis that will be used in the rest of this book. Consequently we shall give no proofs as they can be easily found in all the standard textbooks (for instance , ), with two exceptions: the proof of Milman’s theorem (Theorem 1.1.12) and the nice and simple proof of Machado’s theorem (Theorem 1.1.16) which is a strong extension of the Stone-Weierstrass theorem.
KeywordsBanach Space Probability Measure Extreme Point Convex Space Compact Convex Subset
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