Harnack Extension for Abstract Perron-Stiletjes Integral and Its Application in LSRSS Property

In this work, we give some definitions of continuities with respect to a bilinear triple of Banach spaces which subsequently provide some further properties of the abstract Perron-Stieltjes integral. Moreover, we expand the notion of Harnack extension and Cauchy property for this integral and apply it for investigating a connection of the abstract Perron-Stieltjes integral and LSRSS property in advance introduced.