Publicación: LOGARITHMIC EXPANSION, ENTROPY, AND DIMENSION FOR SET-VALUED MAPS
Fecha
2020
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ITOGI NAUKI I TEKHNIKI. SER. SOVREM. MAT. PRIL. TEMAT. OBZ.
Resumen
WE OBTAIN A LOWER BOUND FOR THE ENTROPY OF A (NOT NECESSARILY INVARIANT) BOREL PROBABILITY MEASURE WITH RESPECT TO AN UPPER SEMICONTINUOUS SET-VALUED MAP AS THE PRODUCT OF THE LOWER DIMENSION OF THE MEASURE AND THE LOGARITHMIC EXPANSION RATE. THIS IS A GENERALIZATION OF THE WELL-KNOWN MEASURE-PRESERVING SINGLE-VALUED CASE.
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We obtain a lower bound for the entropy of a (not necessarily invariant) Borel probability measure with respect to an upper semicontinuous set-valued map as the product of the lower dimension of the measure and the logarithmic expansion rate. This is
