IJPAM: Volume 66, No. 4 (2011)
``Dimitrie Cantemir" University of Târgu Mures
3-5, Bodoni Sándor Street, 540 500, ROMANIA
e-mail: [email protected]
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.
Received: January 3, 2011
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