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Published in:   Vol. 6 Issue 1 Date of Publication:   June 2017

σ Algebra on Cartesian Product of Vertex Measurable Graphs

S. Sanal,Henah. E. Vatsalya

Page(s):   48-50 ISSN:   2278-2397
DOI:   10.20894/IJCOA. Publisher:   Integrated Intelligent Research (IIR)

Let and be two simple graphs. Let ( , 1) and ( , 2) be two vertex measure spaces. In this paper we introduce a σ algebra 1 2, which consists of all vertex induced sub graphs of , and it contains every vertex measurable rectangle graph of the form H1 H2 , H1 ∈ 1 and H2 ∈ 2. Here, we prove 1 2 is the smallest σ algebra of such that the maps and defined by and for all vertex measurable graphs H in and K in respectively are measurable