Vol. 43, No. 3, 1972

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L-orthogonally scattered measures

Kondagunta Sundaresan and Wojbor Woyczynski

Vol. 43 (1972), No. 3, 785–797

Let (X,Σ) be a measurable space and H be a Hilbert space. Let μ be a measure on Σ with values in H such that μ(A) is orthogonal to μ(B) if A,B are disjoint sets in Σ. Such measures are called orthogonally scattered measures and have been extensively studied during the past two decades by several authors. In this paper, the concept of lattice orthogonally scattered measures is introduced, this being a natural analogue of orthogonally scattered measures, when the measure μ takes values in a topological vector lattice. The main purpose of this paper is to study (1) Hahn extension, (2) Representation and (3) Radon-Nikodym theorem of lattice orthogonally scattered measures.

Mathematical Subject Classification 2000
Primary: 28A55
Secondary: 60H99, 28A45
Received: 13 July 1971
Revised: 15 December 1971
Published: 1 December 1972
Kondagunta Sundaresan
Wojbor Woyczynski