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.
