On Projection Properties of Monotone Integrable Functions

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....

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Bibliographic Details
Published inJournal of Advances in Mathematics and Computer Science Vol. 39; no. 3; pp. 29 - 36
Main Author Olwamba, Levi Otanga
Format Journal Article
LanguageEnglish
Published 29.02.2024
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ISSN2456-9968
2456-9968
DOI10.9734/jamcs/2024/v39i31873

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Summary: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.
ISSN:2456-9968
2456-9968
DOI:10.9734/jamcs/2024/v39i31873