Let a probability space (N, F, ), a natural number n E N, and a function...

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Let a probability space (N, F, μ), a natural number n E N, and a function Xo: (N, F) → (R”, BRn) be given. The Dirac measure on BR concentrated at x € Rn is defined by √x (B): = [1, if x € B, 0, if x € BC, 1 for every B E BR.¹ Note that dx (B) = Iß(x), the indicator function of B at the point x. Suppose that (3) μ({w EN: Xo(w) ≤ B})=√x(B), BEBR¹. (2) Prove that Xo = x almost everywhere with respect to μ. Let a probability space (N, F, μ), a natural number n E N, and a function Xo: (N, F) → (R”, BRn) be given. The Dirac measure on BR concentrated at x € Rn is defined by √x (B): = [1, if x € B, 0, if x € BC, 1 for every B E BR.¹ Note that dx (B) = Iß(x), the indicator function of B at the point x. Suppose that (3) μ({w EN: Xo(w) ≤ B})=√x(B), BEBR¹. (2) Prove that Xo = x almost everywhere with respect to μ.

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To prove that Xo x almost everywhere with respect to we need to show that th... View the full answer