A simultaneous solution to two problems of derivatives.
A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
The present paper deals with certain generating functions and recurrence relations for -Laguerre polynomials through the use of the -operator introduced in an earlier paper [7].
Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in , we are led to an integration process over quite general sets with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.
A closed subset of the real line which is right porous but is not -left-porous is constructed.