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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| Published in | Journal of Advances in Mathematics and Computer Science Vol. 39; no. 3; pp. 29 - 36 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
29.02.2024
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| Online Access | Get full text |
| ISSN | 2456-9968 2456-9968 |
| DOI | 10.9734/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. |
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| ISSN: | 2456-9968 2456-9968 |
| DOI: | 10.9734/jamcs/2024/v39i31873 |