An Exploration on a Normed Space called r-Normed Space: Some Properties and an Application

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.