(In Press) On Conditionally Universal Functions with respect to the Walsh system

Abstract

This paper proves theorems on the existence of conditionally universal functions and universal triads with respect to the Walsh system defined by the author, whose the method of proving allows obtaining the novel approach for constructing the universal series by in Walsh system: transform any measurable almost everywhere finite function, by varying its values on a certain set of arbitrarily small measure, to a function such that, after choosing the corresponding signs for the Fourier series terms in the Walsh system of the corrected function, we can achieve the point when the obtained series is a universal series in class all measurable functions.