  We study transition probabilities of generalized functions as introduced by
Colombeau and Gsponer. We formally introduz the study of H. Bohr almost
periodic functions in the generalized context and use them to give exact values
of transition probabilities in dimension 2. We also prove the existence of
transition probabilities, in the generalized sense, for any moderate net $T =
(T_{\varepsilon})$ with $T_{\varepsilon} : \mathbb H \rightarrow \mathbb H$,
$\mathbb H$ a Hilbert space. In particular, we consider the case of selfadjoint
Hilbert-Schmidt operators. This alludes to the possibility of existence of
transition probabilities in the Fock space, in the sense introduced by
Colombeau and Gsponer, if the spectrum of the operators involved are pure
infinities or infinitesimals. This was already indicated in two papers
coauthored by J. Aragona and J.F. Colombeau et. al.
