# A construction of generalized eigenprojections based on geometric measure theory

## Abstract

Let M denote a $\sigma$-compact locally compact metric space which satisfies certain geometrical conditions. Then for each $\sigma$-additive projection valued measure P on M there can be constructed a "canonical" Radon-Nikodym derivative $\Pi: \alpha \mapsto \pi_\alpha$, $\alpha \in M$, with respect to a suitable basic measure $\rho$on M. The family $(\Pi_\alpha)_{\alpha \in M}$ consists of generalized eigenprojections related to the commutative von Neumann algebra generated by the projections $P(\Delta)$, $\Delta$ a Borel set of M.
Original language English Eindhoven Technische Hogeschool Eindhoven 17 Published - 1985

### Publication series

Name Memorandum COSOR 8509 0926-4493

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