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Proof of Measurables

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If delta = (delta_1, ..., delta_d) is a d-tuple of positive numbers delta_i > 0, and E is a subset of R^d, we define delta E by
delta E = {(delta_1 x_1, ..., delta_d x_d) : where (x_1, ..., x_d) belongs to E}.
Prove that delta E is measurable whenever E is measurable, and
m(delta E) = delta_1 ... delta_d m(E).

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This solution helps find proof of measurables.

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