Gradient Flows pp 105-131 | Cite as

Preliminary Results on Measure Theory

Part of the Lectures in Mathematics ETH Zürich book series (LM)


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).


Measure Theory Polish Space Borel Function Borel Probability Measure Transport Plan 
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© Birkhäuser Verlag AG 2008

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