IJPAM: Volume 66, No. 4 (2011)
``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.
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
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4