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

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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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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 23, 2024 10:01 AM

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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

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i Data from lemma 72 ii Because of Lemma 72 ...View the full answer

Measures Integrals And Martingales

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