Let $H$ be a complex [Hilbert space](/page/Hilbert%20Space), and let $a,b\in \mathcal{L}(H)$ be bounded [self-adjoint operators](/page/Self-Adjoint%20Operators). Let $E_a:\mathcal{B}(\mathbb{R})\to \mathcal{L}(H)$ and $E_b:\mathcal{B}(\mathbb{R})\to \mathcal{L}(H)$ denote the spectral projection-valued measures of $a$ and $b$, respectively. If $ab=ba$, then for every pair of Borel sets $A,B\in\mathcal{B}(\mathbb{R})$ one has

\begin{align*} E_a(A)E_b(B)=E_b(B)E_a(A). \end{align*}