Question: Let (E in mathscr{B}(mathbb{R}), Q: E ightarrow mathbb{R}, Q(x)=x^{2}), and (lambda_{E}:=lambda(E cap cdot)) (Lebesgue measure). (i) Show that (Q) is (mathscr{B}(E) / mathscr{B}(mathbb{R}))-measurable. (ii) Find
Let \(E \in \mathscr{B}(\mathbb{R}), Q: E ightarrow \mathbb{R}, Q(x)=x^{2}\), and \(\lambda_{E}:=\lambda(E \cap \cdot)\) (Lebesgue measure).
(i) Show that \(Q\) is \(\mathscr{B}(E) / \mathscr{B}(\mathbb{R})\)-measurable.
(ii) Find \(u \circ Q^{-1}\) for \(E=[0,1], u=\lambda_{E}\) and \(E=[-1,1], u=\frac{1}{2} \lambda_{E}\).
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i Data from lemma 72 ii Because of Lemma 72 ... View full answer
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