遍历变换讲义
Lecture notes on ergodic transformations
AI总结：
本讲义系统介绍了遍历变换的核心理论，涵盖遍历性等价性质、Birkhoff定理、弱混合、典型熵不变量、Poisson悬浮及酉算子谱定理等关键主题。
摘要：
讲义内容如下。与遍历性等价的变换性质。Birkhoff定理。与弱混合等价的性质。变换的典型性质。构造变换的Lego。典型熵不变量。具有完全正P熵的Poisson悬浮。酉算子的谱定理。紧因子，Kronecker代数。弱混合变换的递进回归。遍历变换的双重回归。
英文摘要：
Content of the lectures is the following. Properties of transformations equivalent to ergodicity. Birkhoff's Theorem. Properties equivalent to weak mixing. On typical properties of transformations. Lego to construct transformations. Typical entropy invariants. Poisson suspensions with completely positive P-entropy. Spectral theorem for unitary operators. Compact factors, Kronecker algebra. Progression recurrence for weakly mixing transformations. Double recurrence for ergodic transformations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
