Due Date: Friday, April 8
Let \((X,\mu)\) be a measure space, and let \(\varphi\) be a measure-presrving transformation of \(X\). Prove that if \(f\) is a Lebesgue integrable function on \(X\), then \(f\circ \varphi\) is also Lebesgue integrable, and \[ \int_X (f\circ \varphi)\,d\mu \,=\, \int_X f\,d\mu. \]