A Decomposition of Measures

  title={A Decomposition of Measures},
  author={Norman Y. Luther},
  journal={Canadian Journal of Mathematics},
  pages={953 - 959}
  • N. Luther
  • Published 1968
  • Mathematics
  • Canadian Journal of Mathematics
Let X be a set, a σ-ring of subsets of X, and let μ be a measure on . Following (1), we define μ to be semifinite if We show (Theorem 1) that every measure can be reduced to a semifinite measure for many practical purposes. In many cases, this reduction can be made even more significantly (Theorems 2 and 3). Finally, necessary and sufficient conditions that a semifinite measure be c-finite are given as a corollary to Theorem 3. 
3 Citations

Extensions of tight set functions with applications in topological measure theory

Let X1, J{f2 be lattices of subsets of a set X with X1 C 2. The main result of this paper states that every semifinite tight set function on S1 can be extended to a semifinite tight set function on

Classes of Localizable Measure Spaces

It will be shown that there is a linear order between four of the known and established classes of “localizable measures” and that no pair of the classes within this order coincide.



On the lebesgue decomposition theorem

Berberian, Measure and integration (Macmillan

  • New York,
  • 1965