CHARACTERIZATION OF THE DUAL SPACE OF L1 AND
LEBESGUE DECOMPOSITION FOR NON-σ-FINITE
MEASURE SPACES
LEBESGUE DECOMPOSITION FOR NON-σ-FINITE
MEASURE SPACES
Abstract. The purpose of this paper is to determine the dual space of the
space 
of all Daniell integrable functions and to prove the
Lebesgue decomposition theorem in general measure spaces. In the measure
theory, it is well known that the dual space 
can be
identified with essentially bounded function space
when 
is
-finite, and that the non--finite measure
fails the Lebesgue decomposition. We show, in general, that the element of 
consists of a particular family of
measurable functions. We call this family ``folder'', and the folder
enables us to determine the dual space of 
and to formulate the
general Lebesgue decomposition theorem.
of all Daniell integrable functions and to prove the
Lebesgue decomposition theorem in general measure spaces. In the measure
theory, it is well known that the dual space can be
identified with essentially bounded function space
when is
-finite, and that the non--finite measure
fails the Lebesgue decomposition. We show, in general, that the element of consists of a particular family of
measurable functions. We call this family ``folder'', and the folder
enables us to determine the dual space of and to formulate the
general Lebesgue decomposition theorem.
AMS Subject classification: 28B99, 46B22
Keywords and phrases: non--finite measure, folder, Radon-Nikodym Theorem, localizable
-finite measure, folder, Radon-Nikodym Theorem, localizable
Download full article from here (pdf format).
DOI: 10.12732/ijam.v26i5.8
Volume: 26
Issue: 5
Year: 2013
