Understanding weak values without new probability theory
  The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable $\hat A$ with post-selection $\langle F|$ may be out of the eigenvalue range of $\hat A$. This is because the weak value of $\hat A$ with the post-selection is, in general, not the expectation value of $\hat A$, but the expectation value of $\hat A| F\rangle\langle F|$ boosted by the post-selection. 
Riuji Mochizuki
quant-ph