| Autor: |
Pramada, J., Rao, Y. V. Seshagiri, Rao, T. Nageswara |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 5/11/2023, Vol. 2707 Issue 1, p1-16, 16p |
| Abstrakt: |
This paper is motivated by GABOR SZASZ's introduction of outer measure based on valuation for lattices. We introduce order-preserving valuation on a relative sub lattice of the lattice, a countable cover of an element in a relative sub lattice, outer measure induced by a valuation of a relative sub lattice, Ɲ* measurability and to establish certain elementary properties of induced outer measure via order preserving valuation on a relative sub lattice. To prove outer measure via order preserving valuation on a relative sub lattice is also valid the outer measure generated by measure, we define the definition of outer measure on relative sub lattices of a lattice L induced by a measure Ɲ on Q of relative sub lattices of L, measure on algebra of relative sub lattices and outer measure of relative sub lattices, we prove L(ℬ) is a sigma-algebra where L(ℬ) is the class of Ɲ* measurable relative sub lattices and deduce a corollary that Ɲ*(S) = Ɲ(S), also we prove that outer measure to any subset E of a relative sub lattice SEQσand outer measure to relative sub lattice BEQσδ are equal. Finally, by defining sigma-finite measure on Q and Ɲ* generated by Ɲ we prove a relative sub lattice E is measurable Ɲ* ⇔ E is the proper difference S ∼ B of a relative sub lattice A in Qσδ and a relative sub lattice B with Ɲ*(B) = 0. Further each relative sub lattice B with Ɲ*(B) = 0 is contained in a relative sub lattice C in Qσδ with Ɲ*(C) = 0. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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