On normal and strongly normal lattices

On Normal and Strongly Normal Lattices

In this paper we will investigate the properties of normality and strong normality of lattices and their relationships to zero-one measures. We will eventually establish necessary and sufficient conditions for lattices to be strongly normal. These properties are then investigated in the case of separated lattices.

On strongly normal tesselations

On linear normal lattices configurations

In this paper we extend Champernowne’s construction of normal numbers in base b to the Z case and obtain an explicit construction of the generic point of the Z shift transformation of the set {0, 1, ..., b−1}Zd . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base b .

Normal Characterizations of Lattices

Let X be an arbitrary nonempty set and a lattice of subsets of X such that ∅, X ∈ . Let ( ) denote the algebra generated by and I( ) denote those nontrivial, zero-one valued, finitely additive measures on ( ). In this paper, we discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider the interplay betwe...

« - Normal Lattices William

An rj-normal lattice is a distributive lattice with 0 such that each prime ideal contains at most n minimal prime ideals. A relatively ra-normal lattice is a distributive lattice such that each bounded closed interval is an /¡.-normal lattice. The main results of this paper are: (1) a distributive lattice L with 0 is 71,-normal if and only if for any %n, x,,*•', X e L such that x Ax. = 0 for an...