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Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.

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