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The Characteristics Of Partial Lattices And Irreducibility Of Measurable Functions On Partial Lattice
[Full Text]
AUTHOR(S)
Y.V.Seshagiri Rao, D.V.S.R.Anil Kumar
KEYWORDS
complete measure, locally measurable lattice, saturated, meet irreducible, join irreducible.
ABSTRACT
By defining the principal meanings of locally-measurable lattice, complete-measure, saturated-lattice measure, we demonstrates that each lattice measure space can be incorporated into a complete-lattice measure space also set up an outcome that If ɲ is lattice sigma-finite measure then it is saturated. Also provides the definitions of join (meet) irreducibility of an element of a partial lattice, measurable function on a partial lattice and proves the join (meet) of two measurable functions defined on partial lattice is measurable, the set of all real-valued measurable functions is a vector space as well as lattice. The main object of this paper is if {hn} is an increasing(decreasing) sequence of join(meet) irreducible measurable functions on a partial measurable lattice space (H, B ̅, ɲ) then their join(meet) is join(meet) irreducible measurable function.
REFERENCES
[1] Anil Kumar D.V.S.R., The nature of points in countable Boolean lattice measures.
[2] Birkhoff.G, Lattice Theory 3rd ed., AMS Colloquium Publications, Providence, RI, 1967.
[3] Royden. H.L., Real Analysis, 3rd ed., Macmillan Publishing, New York, 1981.
[4] Rutherford.D.E., Oliver and Boyd Ltd., Tweed dale Court, Edinburgh, London, 1965.
[5] Seshagiri Rao Y.V., Anil Kumar, Characterization of outer measure of partial lattices in a countable Boolean Lattice, ARPN Journal of Engineering and Applied Sciences, Vol.14, No.4, February 2019,ISSN:1819-6608.
[6] Szasz Gabor, Introduction to lattice theory, academic press, New York and London 1963.
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