Operator theory Spectral theorems and functional calculus Concept
Projection-valued measure
Summary
A projection-valued measure assigns to each measurable set an orthogonal projection on a Hilbert space, in a way that is additive like a measure. It is the object that the spectral theorem attaches to a self-adjoint or normal operator, and it allows one to integrate functions against an operator. In quantum mechanics, projection-valued measures describe sharp measurements: the projection of a set corresponds to the event that the measured value lies in that set.
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| Tag | ATGT25E5FF |
|---|---|
| URI | m2://ATGT25E5FF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 47B15, 28B05, 46C05 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Spectral theorem for unbounded self-adjoint operators
- Mathematical formulation of quantum mechanics
- Borel functional calculus
- Spectral theorem for bounded normal operators