Preliminary Results on Measure Theory
In this chapter we introduce, mostly without proofs, some basic measure-theoretic tools needed in the next chapters. We decided to present the most significant result in the quite general framework of separable metric spaces in view of possible applications to infinite dimensional Hilbert (or Banach) spaces, thus avoiding any local compactness assumption (we refer to the treatises [126, 71, 72, 136, 67] for comprehensive presentations of this subject).
KeywordsMeasure Theory Polish Space Borel Function Borel Probability Measure Transport Plan
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