## Ergodic Theory |

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### Contents

3 MeasurePreserving Transformations and Flows | 3 |

Methods of Spectral Analyses | 19 |

Statistical Transformations and Flows | 47 |

1 other sections not shown

### Common terms and phrases

absolute convergence Acad analogous application Approximation Theorem arbitrary fixed arcs assertion assumed average Borel boundary value bounded variation characteristic function considered constant continuous convergence corresponding countably cusps decomposition defined DEFINITI0N eigenelement belonging eigenfrequency eigenfunction equations ergodic flow Ergodic Theorem everywhere exists f and g f belongs f(Pt field F finite measure finite sum FL0WS flow lines follows Fubini Theorem Fuchsian group fundamental domain geodesic lines harmonic function Hilbert space Hopf Individual Ergodic Theorem integral invariant with respect jump discontinuity points limit line elements linear m-measure m-preserving Math measurable function measure-preserving metrically transitive mixing type Neumann nonnegative null set obtain one-to-one pairwise disjoint positive definite Principal Lemma Proc product sets product space proof proved rectangles relative number result satisfies sequence spectral substitutions summable surface Theorem l8.l theory torus transformation Translator's Note unitary operators valid vanishes velocity magnitude wandering set wide sense zero