Question: Need help with problem 2, Real analysis and measure theory course. 2. Let (X, M, u) be a measure space and f : X -

Need help with problem 2, Real analysis and measure theory course.

2. Let (X, M, u) be a measure space and f : X - R a Borel measurable function. Define v on the Borel subsets of R by (E) = u(f (E)). Prove that v is a measure and that, if g: R -> [0, co] is Borel measurable, then f g du = J gof du

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