ИСТИНА

Starting from the classical family of measurable functions on a descriptive space we consider postclassical families of distributable and uniform functions on prescriptive spaces and their applications to Hausdorff-Sierpinski problem of functional description of the uniform closure of the linear space of semicontinuous functions, Riesz-Radon-Frechet problem of characterization of Radon integrals as linear functionals, and a new characterization of Riemann integrable functions.