Question: Let a probability space (N, F, ), a natural number n E N, and a function Xo: (N, F) (R, BRn) be given. The

Let a probability space (N, F, ), a natural number n E N, and a function Xo: (N, F) (R, BRn) be given. The

Let a probability space (N, F, ), a natural number n E N, and a function Xo: (N, F) (R, BRn) be given. The Dirac measure on BR concentrated at x Rn is defined by x (B): = [1, if x B, 0, if x BC, 1 for every B E BR. Note that dx (B) = I(x), the indicator function of B at the point x. Suppose that (3) ({w EN: Xo(w) B})=x(B), BEBR. (2) Prove that Xo = x almost everywhere with respect to .

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