Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0644.28002
Adamski, Wolfgang
On regular extensions of contents and measures. (English)
[J] J. Math. Anal. Appl. 127, 211-225 (1987). ISSN 0022-247X

Let ${\cal K}$ be a lattice of subsets of X. Let N(${\cal K})$ be the family of all [0,$\infty]$-valued set functions defined on ${\cal K}$ and vanishing at $\emptyset$. If $\lambda \in N({\cal K})$ we say $\lambda$ to be modular if $$ \lambda (k\sb 1)+\lambda (k\sb 2) = \lambda (k\sb 1\cap k\sb 2)+\lambda (k\sb 1\cup k\sb 2) $$ and $\lambda$ is said to be supermodular if $$ \lambda (k\sb 1)+\lambda (k\sb 2)\le \lambda (k\sb 1\cap k\sb 2)+\lambda (k\sb 1\cup k\sb 2). $$ It is said to be tight if $$ \lambda (k\sb 2) = \lambda (k\sb 1)+Sup\{\lambda (k)\vert \quad k\in {\cal K},\quad k\subset k\sb 2-k\sb 1\} $$ for $k\sb 1,k\sb 2\in {\cal K}$ with $k\sb 1\subset k\sb 2$. Based on the concept of tight set function and the fact that every supermodular set function defined on a lattice of sets admits a tight majorant, the author generalizes extension theorems due to others including that of his own [Trans. Am. Math. Soc. 283, 353-368 (1984; Zbl 0508.28001)].
[M.K.Nayak]

MSC 2000:: *28A12 Measures and their generalizations

Keywords: tight set function; supermodular set function; tight majorant; extension theorems

Citations: Zbl 0508.28001

Cited in: Zbl 0772.28001

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]