Local entropy averages and projections of fractal measures
نویسندگان
چکیده
منابع مشابه
Local Entropy Averages and Projections of Fractal Measures
We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of self-similarity under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We apply this to prove the following conjecture of Furstenberg: if X,Y ⊆ [0, 1] are closed and invariant, respectively, under ×m mod 1 and ×n mod 1, where m,n are not...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.175.3.1