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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Convergence of metric-measure spaces
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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.