The Extension Theories Based on Regularity

Heinz König ()
Additional contact information
Heinz König: Universität des Saarlandes, Fakultät für Mathematik und Informatik

Chapter CHAPTER II in Measure and Integration, 1997, pp 33-78 from Springer

Abstract: The theme of the present chapter is the construction of contents and measures from more primitive set functions. The construction is based on interrelated regularity and continuity conditions. These conditions are either both of outer or both of inner type. We want to demonstrate that the outer and inner theories are identical. To achieve this we have to work with the unconventional notions introduced in the first chapter, with set systems which avoid the empty set like the entire set, and with isotone set functions which take values in ℝ or $\overline{\mathbb{R}}$ . We start with the complete development of the outer extension theory. Then the upside-down transform method initiated in the first chapter will transform the outer into the inner extension theory. The chapter concludes with a detailed bibliographical annex.

Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-89502-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9783540895022

DOI: 10.1007/978-3-540-89502-2_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().