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math.CA2011★ 6 cited
Porosity, dimension, and local entropies: a survey
Pablo Shmerkin
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationsh…
math.CA2011★ 5 cited
Dimension, entropy, and the local distribution of measures
Tuomas Sahlsten, Pablo Shmerkin, Ville Suomala
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generaliz…