New results on integration on the Levi-Civita field
The Levi-Civita field \(\mathcal R\) consists of functions \(f: \mathbb Q\to \mathbb R\) whose supports are left-finite, that is there is only a finite set of support points to the left of any given one. The paper is a continuation of an earlier one, by \textit{K. Shamseddine} and \textit{M. Berz} [Contemp. Math. 319, 369--387 (2003; Zbl 1130.12301)], devoted to the integration theory for \(\mathcal R\)-valued functions on subsets of \(\mathcal R\). The author proves that the integrals of functions coinciding almost everywhere are equal and that the uniform convergence preserves the measurability of functions and the values of their integrals. Thus main properties of integrals over \(\mathcal R\) are similar to those of the classical counterparts.
scientific article; zbMATH DE number 6121469
scientific article