IJPAM: Volume 66, No. 4 (2011)

SOME APPLICATIONS OF PRINCIPLE OF DIVISION

Gheorghe Chivu
Dimitrie Cantemir" University of Târgu Mures
3-5, Bodoni Sándor Street, 540 500, ROMANIA
e-mail: chivu_1955@yahoo.com

Abstract.A survey of known results, from integration theory is presented, showing that many theorems can be proved using a principle of division''.

Let denote Lebesque measure on . If is a compact set in if is a Banach space, and if , then the Bochner integral of is the unique set function from to which is -additive and which fulfills an infinitesimal condition with respect to Finally we use the Principle of division'' to prove a changing variables theorem.

AMS Subject Classification: 31D05, 60J45

Key Words and Phrases: compact set, -division, basis of compact sets, additive set functions, subadditive set functions, basis of filter, infinitesimal condition, principle of definition

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4