A NOTE ON A PETTIS-KURZWEIL-HENSTOCK TYPE INTEGRAL IN RIESZ SPACES

Abstract Recently a connection has been found between the improper KurzweilHenstock integral on the real line and the integral over a compact space. In this paper these results are extended to a Pettis-type integral for the case of functions with values in Riesz spaces with "enough" order continuous functionals

The Kurzweil construction of an integral in ordered spaces

summary:This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper