ENTROPY VALUES OF CHAINS OF PARTITIONS
OF INFINITE COUNTABLE SETS

SERVET MART´NEZ AND JAIME SAN MART´N

Abstract:

We study the structure of the chains of partitions of countable sets. Our main result asserts that for any chain and any probability measure the set of entropy values is a totally disconnected set in with null-Lebesgue measure. The complexity of the set is exhibited in an example where is a Cantor set with non null Hausdorff dimension.