The finitary coding of two Bernoulli schemes with unequal entropies has finite expectation
type: Item
instance of: scholarly article
title: The finitary coding of two Bernoulli schemes with unequal entropies has finite expectation
zbMATH Open document ID: 0894.28010
DOI: 10.1016/S0019-3577(97)89136-7
published in: Indagationes Mathematicae. New Series
publication date: 1997-03-11T00:00:00Z
review text: \textit{M. Keane} and \textit{M. Smorodinsky} [Isr. J. Math. 26, 352-371 (1977; Zbl 0357.94012)] constructed a finitary coding between two Bernoulli schemes with unequal entropy (a coding between sequence spaces is called finitary if after removing sets of measure zero from both spaces it is continuous on the remaining sets). It was mentioned in their paper that the coding has finite expectation (i.e., the averge number of coordinates in the larger entropy scheme needed to determine one coordinate in the image point is finite). However, M. Keane informed the author of the article under review that they had no proof of this fact. The aim of this paper is to supply this proof.
reviewed by: Geoffrey R. Goodson
Mathematics Subject Classification ID: 28D20
zbMATH DE Number: 989753
zbMATH Keywords: Bernoulli shift
zbMATH Keywords: finitary coding
zbMATH Keywords: Bernoulli schemes
zbMATH Keywords: entropy
author: J. Serafin
MaRDI profile type: Publication
cites work: A class of finitary codes
cites work: Factors of Bernoulli shifts are Bernoulli shifts
full work available at URL: s0019-3577(97)89136-7
OpenAlex ID: W2044037947
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description: scientific article; zbMATH DE number 989753