Let $B=\int_{Y}^{\oplus}B_yd_y$ be the direct integral decomposition of vNa $B$ into factors and if $P=\int_{Y}^{\oplus} p_ydy$ is a projection in $B$ and $p_y$ is equivalent to a projection $q_y$ in $B_y$ for all or a.e. $y\in Y$. Is there a good choice of $q_y$ up to equivalence such that $Q=\int_{Y}^{\oplus} q_ydy$ makes sense and $P$ and $Q$ are equivalent in $B$?

Suppose B is a trivial bundle whose fibers are type I_{2} factors and p is a constant section of B corresponding to some projection with 1dimensional image. Projections with 1dimensional image in a type I_{2} factor can be identified with angles, i.e., elements of iR/πiZ. If q is given by some nonmeasurable section of B, then there is no way to choose its equivalence class in such a way that Q exists. 

