On Projection Properties of Monotone Integrable Functions
Levi Otanga Olwamba · Journal of Advances in Mathematics and Computer Science · 2024
This research formulates an \((i-1, i)\) - dimensional structure of \(\mu_{|f|^p}^{(i-1, i)}\)-vector measure integrable functions for \(i=1,2, \ldots n\). 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 \(\Pi_i A_{i-1}^{(i, i+1)}\) are partitioned into disjoint sets \(\Pi_i A_{i-1}^i\) 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.