By Yasui Y.

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**Additional resources for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono**

**Example text**

In that example, it is not appropriate for player I simply to choose D and then ignore what happens in the subgame that is reached with zero probability. 3. 1. Preliminaries Let 0 be the non-empty sample space 0, which may be finite or infinite. ): P(O) -+ [0,1] C 91 which are defined on the power set P(O) of all subsets of 0 and which, for some non-empty finite set F C 0, satisfy the two restrictions that (1) p(E) = p(E n F) (all E C 0) and p(F) = 1. It loses no generality to suppose that F has been chosen to satisfy p( w) > 0 for all w E F, in which case F is called the support of p(.

So the three spaces must be equivalent, as claimed. 2. Homeomorphic Metric Spaces A collection of metrics for each of the three spaces of extended probabilities ~L(F), ~e(F), and ~M(F) will now be constructed in a way that creates a homeomorphism between each pair of spaces. This collection will be based upon the particular metric dc for the space ~e(F) which is defined, for all pairs P, Q E ~e(F), by de( P, Q) (25) := max {Ip({w} I {w,w'})-Q({w} I {w,w'})/}. w,w'EF After this definition for ~e(F), the metrics on the other two spaces will be constructed to ensure that homeomorphism is automatically satisfied.

Moreover, this property holds when additivity is weakened to the subadditivity of upper probability measures or the superadditivity of lower probability measures. I give the simple proof for upper probability measures. First, define conditional upper probability in the usual way: if P*(B) > 0 then P*(A I B) = P*(AB)/ P*(B). CONTRIBUTIONS TO THE FORMAL THEORY OF PROBABILITY Then if P*(BC) 23 >0 P*(AB I C) P*(ABC)/P*(C) P*(A I BC)P*(B I C)P*(C)/P*(C) P*(A I BC)P*(B I C) The point of the proof is to show that additivity is not required, only the definition of conditional probability and the Boolean properties of events.

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

by Jason

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