In the following cases, check whether Pn < Qn or Qn Pn (or both) hold. (a)...

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In the following cases, check whether Pn < Qn or Qn Pn (or both) hold. (a) Pn = U([0, 1]) and Qn = U([0,1 + 1/2]) on (R, B (R)). (b) Pn = U([0,1])n and Qn = U([0, 1+ 1])n on (Rn, B (R")). Definition 7.11. Let (Pn) n1 and (Qn) n1 be two probability measures on a sequence of measurable spaces (Xn, Bn). We say that (Qn) n1 is contiguous with respect to (Pn) n1 if for every sequence An Bn with limn Pn[An] 0, we also have limn Qn[An] = 0. In this case we write Qn In the following cases, check whether Pn < Qn or Qn Pn (or both) hold. (a) Pn = U([0, 1]) and Qn = U([0,1 + 1/2]) on (R, B (R)). (b) Pn = U([0,1])n and Qn = U([0, 1+ 1])n on (Rn, B (R")). Definition 7.11. Let (Pn) n1 and (Qn) n1 be two probability measures on a sequence of measurable spaces (Xn, Bn). We say that (Qn) n1 is contiguous with respect to (Pn) n1 if for every sequence An Bn with limn Pn[An] 0, we also have limn Qn[An] = 0. In this case we write Qn

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