## Selecta: expository writing |

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### Contents

ENTROPY IN ERGODIC THEORY1 PAUL R HALMOS CONTENTS Preface | 24 |

Conditional Expectation | 25 |

Examples | 26 |

Copyright | |

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Acad Amer American Mathematical analysis analytic answer applied mathematics assertion Banach spaces bounded Bourbaki called compact complete complex number computable concept conjecture convergence defined definition differential easy elementary elements entropy equations ergodic theorem event everywhere example exists fact finite finite-dimensional follows geometry Hilbert space homeomorphic implies indecomposable infinite instance integrable intuitive invariant subspaces invertible isomorphic known lattice Lebesgue lecture linear transformation logic machine manifolds Math mathematician matrix mean measurable function measurable set measure preserving transformation measure space measure zero measure-preserving transformations Monthly Neumann non-trivial normal P. R. Halmos paper polynomials positive integer problem Proc proof properties proved pure question random variables result Riesz Section sense sentence sequence solution spectral theorem statement subfield subset thing tion Toeplitz operators topological trivial unilateral shift unitary dilation unitary equivalence unitary operator vector space words write