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Why do weak and L metric topology for measures coincide?

Let $(X,d)$ be a complete metric space, $$M^1 := \{\mu: \mu \mbox{ is a Borel regular measures having bounded support and } \mu(X) = 1\},$$ and $$BC(X) := \{f : f:X\rightarrow \mathbb{R} \mbox{ is …
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3 votes
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299 views

Covering lemmas in Hochman's ''On self-similar sets with overlaps and inverse theorems for e...

I am confused about the covering lemmas in the captioned work and really hope to get some ideas here. Firstly it is lemma 3.7. (Image of Lemma 3.7) (for convenience here is the lemma of this lemma (I …
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