On singularity and Lebesgue type decomposition for operator-valued measures

V. Mandrekar and H. Salehi

Journal of Multivariate Analysis, 1971, vol. 1, issue 2, 167-185

Abstract: The concepts of absolute continuity and singularity for operator-valued measures are introduced and Radon-Nikodym and Lebesgue decomposition theorems for such measures are established. These theorems reduce directly to the classical results in the scalar case. The results have interesting applications to the theory of infinite-dimensional stationary stochastic processes.

Keywords: Operator-valued; measure; absolute; continuity; singularity; Radon-Nikodym; theorem; Lebesgue; type; decomposition; theorem; stationary; stochastic; processes (search for similar items in EconPapers)
Date: 1971
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