Partial measures

2000/05/07 by O. E. Tikhonov
Mathematics · #math.FA #msc:28A10

paper · pdf

published as Lobachevskii Journal of Mathematics 6 (2000), 47-50 ( http://ljm.ksu.ru ). · 4 pages. Submitted to Lobachevskii Journal of Mathematics ( http://ljm.ksu.ru)

arxiv created 2000/05/07 · arxiv updated 2009/11/30

Abstract

We study sigma-additive set functions defined on a hereditary subclass of a sigma-algebra and taken values in the extended real line. Analogs of the Jordan decomposition theorem and the Radon-Nikodym theorem are obtained.

Related

• Finitely additive functions in measure theory and applications
• An elementary proof of representation of submodular function as an supremum of measures on σ-algebra with totally ordered generating class
• On a theorem of Pelc and Prikry on the nonexistence of invariant extensions of Borel measures
• Closed and sigma-finite measures on the orthogonal projections
• On a theorem of Banach and Kuratowski and K-Lusin sets