Modes of Convergence: Interpolation Methods I Original Research Article

In the present paper we explore an approximation theoretic approach to some classical convergence theorems of real analysis. The background of this paper is the intuition that some of the usual compactness theorems on various modes of convergence in classical analysis are based on suitable ways of obtaining good decompositions of functions to exploit rates of approximation, cancellations, or appropriate control of sizes that can be controlled by the basic functionals of real interpolation.