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如何建模值得思考 Abstract: Rohlin's Lemma which was originally (cf [18]) proved for bi-measurable aperiodic automorphisms T of a Polish space X is a basic tool in ergodic theory. It states that for an automorphism of the above type which is invariant with respect to a Borel probability measure /& any r~ c N+ and any e > O, one can find a measurable set R ( a so called (r; of A TER。。TERremainder,e) Rohlin set) such that, for ] 0, 1, ..., r; 1, the sets T JR are pairwise disjoint and exhaust X with exception set whose mass is smaller than e. In particular, Rohlin's Lemma is indispensable for the canonical construction of generators. Since the classical proof (cf [11]) quoted in the standard textbooks on ergodic theory (e. g., [7], [9], [17]) uses a Kakutani tower type construction and thus needs forward measurability, we feel obliged to provide an elementary proof which doesn't rely on this assumption. Moreover, the setting is generalised from Polish space to separable space. Here we improve ...............
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