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Extra info for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono

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Equivalence relation We define an on ~i by ~I ~ 72 if ~l(T f) = ~2(r f) for all f in LI[~ ]. H I is the collection of all equivalence classes from ~i. In the case B is a Hilbert space, H, let ~2 be the set of all complex-valued finite measures on H that are absolutely continuous with respect to ~. complex numbers. ~l and H2 are linear spaces over the By a linear variety in B we mean a set of the form S + m, where m c B and S is a closed linear manifold. Theorem 2: (i) If for any x in B* there then ~ << ~ if and only if G: ~ ÷ exists f in LI[~ ] such that [T f](x) ~ 0, ~(~) is continuous on ~I in the range(T ) topology.

Then the set \$ is abundant Proof: in the strict sense. To simplify the terminology, if the process (Xn)n~N satisfies P(k) at ~, we shall say that P(k) holds at ~. It is easily verified that the set S satisfies properties tion 2. a) and b) of Defini- It remains to check the density property c): For each T f Tf define ~' by T'(~)) = inf{k f N I k > T(m) It follows from the assumptions and P(k) holds at ~}. that T' £ Tf. Moreover the relation T ~ n implies that the set {T' = T} includes tile set Bn= ~ k>n ~- For the latter we have by assumption P(Bn) ~ i.

2 we need only show on E. 6) is equivalent to {x: ]ll IT, > I] r l+pU(au)" llxll= and We use the fact that r = II1 xlll T' > 1 i s Therefore equivalent u = III to xlHx11=, x # III T' > ~ 0, to see that or Ilxll= = r > 1/]l~lll~,. 6). We write {x: I] Ill T'--

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### A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono by Yasui Y.

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