Question: qn. 4 4. Show that every function X on is measurable with respect to the power set of . 5. We have seen that if

qn. 4 4. Show that every function X on is measurable

qn. 4

4. Show that every function X on is measurable with respect to the power set of . 5. We have seen that if Y is a function of X,Y induces a sub- -field of that induced by X. Is the converse true? Can you prove that there exists of Borel function g such that Y=g(X), in the case X is real valued? (Hint: Borel field has a countable number of generators)

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