Affiliation:
1. Department of Mathematics , University of Allahabad , Allahabad , 211 002 , India
Abstract
Abstract
The aim of the present paper is to study lattice outer measures on an unsharp quantum logic, viz. a difference poset P associated with a monotone function μ defined on a sub-difference poset L of P and an approximating family in L. Having proved a number of fundamental properties, relationships among these outer measures and eventually among corresponding families of measurable elements of P are investigated.
Reference30 articles.
1. Adamski, W.: On extremal extensions of regular contents and measures, Proc. Amer. Math. Soc. 121 (1994), 1159–1164.
2. Avallone, A.—Basile, A.: On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378–390.
3. Avallone, A.—De Simone, A.: Extensions of modular functions on orthomodular lattices, Ital. J. Pure Appl. Math. Soc. 9 (2001), 109–122.
4. Balcar, B.—Jech, T.: Weak Distributivity. A Problem of Von Neumann and the Mystery of Measurability, Bull. Symb. Logic 12(2) (2006), 241–266.
5. Beltrametti, E. G.—Cassinelli, G.: The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, 1981.