A projection-valued measure (PVM) is a fundamental concept in the fields of functional analysis and quantum mechanics, particularly in the mathematical formulation of quantum theory. It is a specific type of measure that assigns a projection operator to each measurable set in a given σ-algebra.
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A projection-valued measure assigns an orthogonal projection to each measurable set, with , , , and countable additivity in the strong operator topology on pairwise disjoint sets.