(POV measure) $B$ has a value from a set $E$. For ordinary observables $B$ and singleton sets $E=\{b\}$, the ‘effect’ $B(E)$ reduces to a projector $\Pi_b$. Equation contains a special case of only,

[ll]{} P\_[ab]{}&=\_a\_b / \_a\
&= a|\_b|a= |a|b|\^2    \_a=|aa|, a|a=1.

It is interesting to note that Wigner’s formula reappears as the basic formula in the theories of consistent histories (e.g., equation (4.3) in [Omn[è]{}s]{} [@Omn]). However, as mentioned on p.143 of [@Omn], only the case of two reference times can be proved, and this is equivalent to (with $\rho$ replaced by $E_1\rho E_1$, the mixed state obtained after the first state reduction).

However, we can give the probability an alternative, correct meaning: If $a$ is a pure state then implies that $P_{abcd}$ is the probability of measuring $\Pi_a\Pi_b\Pi_cD\Pi_c\Pi_b\Pi_a$ in that state! In general, therefore, Wigner’s formula gives the probability of measuring in state $a$ the last element in a finite sequence $A$, $\Pi_aB\Pi_a$, $\Pi_a\Pi_bC\Pi_b\Pi_a$, $\Pi_a\Pi_b\Pi_cD\Pi_c\Pi_b\Pi_a$, $\dots$, assuming that the measurements resulted in reductions of the intermediate states to the states represented by the projectors $\Pi_a, \Pi_b, \Pi_c, \dots$.

To see how we can possibly interpret this in terms of the uncontroversial part of quantum mechanics, we consider a 