On Projection Properties of Monotone Integrable Functions

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.