منابع مشابه
Outer Measures on a Linear Lattice
In this paper we define and discuss the theory of abstract outer measures on a sequentially continuous(2) linear lattice S. This is a generalization of the concept of outer measure on a function space as used by Bourbaki [3]. H. Nakano [7] and M. H. Stone [8] have modernized Lebesgue's extension theory; our approach provides a common generalization of their theories. We show, for example, that ...
متن کاملCharacterizations of Outer Measures Associated with Lattice Measures
Let ν be a finite countably subadditive outer measure defined on all subsets of a set X, take a collection C of subsets of X containing X and ∅, we derive an outer measure ρ using ν on sets in C. By applying this general framework on two special cases in which ν = μ′′, one where μ ∈ Mσ(L) and the other where μ ∈ Mσ(L1), L1 ⊆ L2 being lattices on a set X, we obtain new characterizations of the o...
متن کاملAPPLICATIONS OF OUTER MEASURES TO SEPARATION PROPERTIES OF LATTICES AND REGULAR OR o - SMOOTH MEASURES
Associated with a 0-1 measure E I(-.) where is a lattice of subsets of X are outer measures/’ and ; associated with a o-smooth 0-1 measure # E Io() is an outer measure " or with Io(.Y’), ’ being the complementary lattice, another outer measure I. These outer measures and their associated measurable sets are used to establish separation properties on o and regularity and a-smoothness of . Separa...
متن کاملLattice Models and Fractal Measures
XXX OBSOLETE XXX HALF-BAKED XXX The ideas described herein are confusingly presented, and are half-baked, incomplete, incoherent. Essentially all the ideas herein are presented more sensibly, more coherently in other papers on this website. Much of what was originally in this paper has been edited out, and moved to another paper, which presents the ideas in a much clearer fashion: see [9]. XXX ...
متن کاملLattice Theory, Measures and Probability
In this tutorial, I will discuss the concepts behind generalizing ordering to measuring and apply these ideas to the derivation of probability theory. The fundamental concept is that anything that can be ordered can be measured. Since we are in the business of making statements about the world around us, we focus on ordering logical statements according to implication. This results in a Boolean...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1992
ISSN: 0022-247X
DOI: 10.1016/0022-247x(92)90328-b