The finitary coding of two Bernoulli schemes with unequal entropies has finite expectation
\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.
scientific article; zbMATH DE number 989753