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  3. let f be measurable and b a borel set. then f-1[b]

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set....

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Advance Math

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set. [Hint: The class of sets for which f-1[E] is measurable is a ?-algebra.

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Proof Let E f1E is Lebesgue measurable Since inverse images are well behaved with respect to all the usual set operations and the family of Lebesgue measurable sets is a algebra it is easy to see that is a algebra Here are the details of that Suppose E Then f1E is Lebesgue measurable Consequently f1E f1E    See Answer
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