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. https://doi.org/10.1016/j.jmaa.2013.12.030
Published in
Journal of Mathematical Analysis and ApplicationsDate
2014Copyright
© 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.
Publisher
Academic PressISSN Search the Publication Forum
0022-247XKeywords
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https://converis.jyu.fi/converis/portal/detail/Publication/23634622