Spaces of Measurable Transformations
نویسندگان
چکیده
By a space we shall mean a measurable space, i.e. an abstract set together with a F: FXX—^Y the natural mapping defined by $F( /> #)=ƒ(#)• A structure R on F will be called admissible if Fl considered as a mapping from the product space (F, R)XX into F, is a measurable transformation. I t may not be possible to define an admissible structure on F; if it is, F itself will also be called admissible. We are concerned with the problem of characterizing, for given X and F, the admissible sets F and the admissible structures R on the admissible sets. The following three theorems may be established fairly easily:
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