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3) where V; is the operator in C'(Y) that is dual to Vr . e. 4) as shown in the diagram '2:"~K(Y) R~,l 1 V; '2:" ~ K(Y). 4) follows particular III § 4 Transformations of Preparation and Registration Procedures for all the 'j introduced above. Since 41 V:. is norm continuous, we conclude V:. Km CY) c: Km CY) . 5) Since V:. is even a(C' (y), C(Y»-continuous, V:. 6) also holds. If differs little from 'j' also the probabilities for rpm (R~,. if) and rpm (R~,; if) must differ but little. For physical reasons we thus must in fNT", assume that V" rpm (if) with fixed Ii is norm continuous relative to ,.

3. This Rr maps the set iilom order isomorphically onto a subset of iilom and maps the Boolean ringiilm (eo) = {el e ~ eo E iilom } isomorphically onto iii (R r eo). The physical interpretation of Rr shall be that the registration method Rr eo arises by applying the method eo a time r later (for fixed preparation). 1. 2) onto itself. 1, then fey) = IfIm(eo, e) = AMeas (y; eo, e)· Therefore, if one shall represent Rr (eo, e) as the registration displaced just by r, then/' (y) = IfIm (Rr(eo, e» must obey /' (y) = f(T r y) with the above T..

F+-f-=fi-h, where f+ is the positive and f- the negative part of fi -f2. This is to say E L(Y) while f+ and f- are equal to zero on Sm, so that sf+ = sf- = o. m(u,j) =0 for all u E Km(Y). j = O. :) = Hence. the ~.. 3 Further Transformations of Preparation and Registration Procedures Here we will make remarks about other transformations possibly defined in &'3',;" but without aspiring an exact formulation. For this purpose one must realize that for preparation and registration devices it is pertinent, how they are oriented to a laboratory coordinate system.

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