Journal ArticleDOI
Invariant measures for many-one transformations
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This article is published in Duke Mathematical Journal.The article was published on 1956-09-01. It has received 45 citations till now. The article focuses on the topics: Invariant (mathematics) & Invariant measure.read more
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On finite limit sets for transformations on the unit interval
TL;DR: An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.
Book
Probability, random processes, and ergodic properties
TL;DR: Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing and will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists.
Journal ArticleDOI
On the structure and diversity of rational beliefs
TL;DR: In this paper, the theory of expectations is reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy and form probability beliefs based on the data generated by the economy, and it is shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy.
Journal ArticleDOI
Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
Journal Article
Information Sources Using Chaotic Dynamics
TL;DR: In this paper, the Bernoulli shift is a fundamental theoretic model of a sequence of independent identically distributed (i.i.d.) binary random variables, and several kinds of linear feedback shift register sequences have been proposed.