Local dimensions of measures on infinitely generated self-affine sets
Rossi, E. (2014). Local dimensions of measures on infinitely generated self-affine sets. Journal of Mathematical Analysis and Applications, 413 (2), 1030-1039. doi:10.1016/j.jmaa.2013.12.030 Retrieved from http://www.sciencedirect.com/science/journal/0022247X/413/2
Published inJournal of Mathematical Analysis and Applications
© Elsevier. This is a final draft version of an article whose final and definitive form has been published by Elsevier.
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space.
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