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An Exploration on a Normed Space called r-Normed Space: Some Properties and an Application
Version 1
: Received: 26 October 2023 / Approved: 27 October 2023 / Online: 27 October 2023 (11:08:25 CEST)
How to cite: Purnawan, R. An Exploration on a Normed Space called r-Normed Space: Some Properties and an Application. Preprints 2023, 2023101770. https://doi.org/10.20944/preprints202310.1770.v1 Purnawan, R. An Exploration on a Normed Space called r-Normed Space: Some Properties and an Application. Preprints 2023, 2023101770. https://doi.org/10.20944/preprints202310.1770.v1
Abstract
In this paper, we explore a new norm on Lp-space called r-norm, and hence producing a new normed space called r-normed space. Measure theoretic and functional analytic properties are covered such as the relation between r-norm and the classical p-norm. An application of r-normed space in probability theory and statsitics is also presented, notably, its role as a rigorous framework in describing the coefficient of determination.
Keywords
r-normed space; r-norm; Lp-space; measure theory; functional analysis; coefficient of determination
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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