On Projection Properties of Monotone Integrable Functions

This research formulates an
- dimensional structure of
-vector measure integrable functions for
. 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
are partitioned into disjoint sets
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.