Let $H$ be a complex [Hilbert space](/page/Hilbert%20Space) and let $T\in\mathcal L(H)$ be normal. Then there exists a unique projection-valued measure
where the essential supremum is taken with respect to the spectral measure class determined by $E$, namely the null Borel sets are exactly those $B\in\mathcal B(\sigma(T))$ for which $E(B)=0$.