=+33.16. 32.13 | Suppose that X has distribution u. Now P[AlX] = f(X(w)) for some Borel function

Question:

f. Show that lim ,, - . P[ Alx -h < X≤x+h] =f(x) for x in a set of u-measure 1. Roughly speaking, P[Ax -h

= x]. Hint: Take v(B) = P(An[X€ B]) in Problem 32.13.

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