Archiv der Mathematik

, Volume 92, Issue 5, pp 438–450

Measure theory based on lattices and transfinite recursion

Article

DOI: 10.1007/s00013-009-2862-6

Cite this article as:
Deiser, O. Arch. Math. (2009) 92: 438. doi:10.1007/s00013-009-2862-6

Abstract.

In this methodological study we develop the foundations of measure theory using lattices as prime structures instead of rings. Topological as well as abstract regularity is incorporated into this approach from the outset. The use of inner and outer measures is replaced by transfinite constructions. Basic extension steps are transfinitely iterated to yield generalizations of Carathéodory’s theorem which are optimal with respect to inner and outer approximations.

Mathematics Subject Classification (2000).

28A1228C2006B99

Keywords.

Contentsmeasuresextensionlatticesregularitytransfinite recursionmodular functions

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany