Abstract
The central question in this chapter is the following:What does it mean to say that a metric-measure space (X, d x , vx ) is “close” to another metric-measure space (Y, d y , vy )? We would like to have an answer that is as “intrinsic” as possible, in the sense that it should depend only on the metric-measure properties of X and Y.
So as not to inflate this chapter too much, I shall omit many proofs when they can be found in accessible references, and prefer to insist on the main stream of ideas.
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© 2009 Springer-Verlag Berlin Heidelberg
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Villani, C. (2009). Convergence of metric-measure spaces. In: Optimal Transport. Grundlehren der mathematischen Wissenschaften, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71050-9_27
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DOI: https://doi.org/10.1007/978-3-540-71050-9_27
Publisher Name: Springer, Berlin, Heidelberg
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