Let S = R[0,1], the set of functions from [0, 1] to R, and let F be the σ-field generated by the cylindrical sets. The purpose of this exercise is to show that the elements of F depend on only...


Let S = R[0,1], the set of functions from [0, 1] to R, and let F be the σ-field generated by the cylindrical sets. The purpose of this exercise is to show that the elements of F depend on only countably many coordinates.


Let
  the set of sequences taking values in R. Let F0
be the σ-field generated by the cylindrical subsets of RN, where N = {1, 2,...}.


Show that B ∈ F if and only if there exist t1,t2,... in
  and a set
 such that











May 22, 2022
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