Mean topological dimension

DOI10.1007/BF02810577zbMath0978.54026WikidataQ60895005 ScholiaQ60895005MaRDI QIDQ1972368

Benjamin Weiss, Elon Lindenstrauss

Publication date: 1 February 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

topological entropymean dimension

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Ergodic theory and statistical mechanics
• An inverted tower of almost 1-1 extensions
• Entropy and isomorphism theorems for actions of amenable groups
• A ratio limit theorem for a strongly subadditive set function in a locally compact amenable group
• Averaging strongly subadditive set functions in unimodular amenable groups. I
• Mean dimension, small entropy factors and an embedding theorem
• Lowering topological entropy
• A proof of Beboutov's theorem
• Can one always lower topological entropy?

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