Separable normed vector space

Reference no: EM13990666

1. Let P be a law on a separable normed vector space (S, · ), x ∈ S, and Px the translate of P by x , so that Px ( A) := P( A - x ) for all Borel sets A, where A - x := {a - x : a ∈ A}. Show that W ( P, Px ) = x.

2. For a separable metric space (S, d) and 1 ≤ r ∞ let Pr (S) be the set of all laws P on S such that ( d(x, y)r dP(x ) <>∞ for some y ∈ S. Show that the same is true for all y ∈ S.

Reference no: EM13990666

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