Let $H$ be a [Hilbert space](/page/Hilbert%20Space), let $K$ be a compact [metric space](/page/Metric%20Space), and let $E:\mathcal{B}(K)\to\mathcal{L}(H)$ be a projection-valued measure. Define the support of $E$ by
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\begin{align*}
\operatorname{supp}(E)
=
\{x\in K:\ E(U)\ne 0 \text{ for every open neighbourhood } U\subset K \text{ of } x\}.
\end{align*}