Lectures on Ergodic TheoryCourier Dover Publications, 15 de nov. 2017 - 112 pàgines This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects. |
Continguts
| 1 | |
Pointwise convergence | 18 |
Consequences of ergodicity | 31 |
Discrete spectrum | 46 |
Weak topology | 61 |
Uniform approximation | 74 |
the problem | 87 |
| 101 | |
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abelian group antiperiodic arbitrary assert automorphism bilateral Borel Cartesian product category theorem characteristic function compact abelian group conjugacy conjugate constant function defined denote discrete spectrum dyadic interval dyadic rational dyadic sets ergodic measure-preserving transformation ergodic transformations exists a measurable f and g f(Tx fact finite measure follows function f Hilbert space infinite interval of rank invariant function invariant measure invariant set invertible measure-preserving transformation isometry isomorphic lemma linear measurable function measurable set measurable subset measurable transformation measure algebra measure space measure zero measure-preserving trans mixing transformations multiplication non-negative non-singular orbit pairwise disjoint permutation positive integer positive measure problem of invariant proper function proper value proper vector recurrence theorem result sequence space set F sets of measure sigma-bounded sigma-finite space of finite subinterval of rank sufficient to prove Suppose tion uniform topology union unit interval unitary operator unitary operator induced weak topology weakly mixing write