Projection-valued measure
= Projection-valued measure
{title2=$E$}
{wiki}
A projection-valued measure $E$ assigns an <orthogonal projection> $E(B)$ to each measurable set, with $E(\varnothing)=0$, $E(X)=I$, $E(B\cap C)=E(B)E(C)$, and countable additivity in the <strong operator topology> on pairwise disjoint sets.