Abstract:
This research formulates an (i − 1, i) - dimensional structure of µ
(i−1,i)
|f|p -vector measure integrable functions
for i = 1, 2, ...n. Fixed point projection properties of a vector measure are appplied to determine the
measurability of sets in the domain of integrable functions. Measurable sets of the form ΠiA
(i,i+1)
i−1
are
partitioned into disjoint sets ΠiA
i
i−1 of finite measure.The obtained results demonstrate utility of concepts
of vector measure duality, continuity from below of a measure and monotonicity of a vector measure in
integrating functions.
