Funciones abstractas de p–variación acotada - Puig de Dios, Yunied (2007)
This investigation dedicates to extend the results of Gelfand regarding the abstract functions of bounded variation to the abstract functions of bounded p-variation in a sense similar to the Theorem of Representation of Riez, with the objective of applying this extension to the study of the space of the absolutely p-continuous functions. In this work the spaces of the abstract functions of strong and weak bounded p-variation in an interval are introduced and their main properties are studied. The abstract integral of Stieltjes is defined in the search of a theorem similar to that of Representation of Riesz and a representation of the continuous lineal operators of the space of the absolutely p-continuous functions on an interval in a normed weakly complete space through the abstract functions of bounded p-variation is found.