The Burkill-Cesari integral for Riesz spaces

A definition of Burkill-Cesari type integral is given, for set functions, taking values in Dedekind complete Riesz spaces. The concepts of quasi-additivity and quasi-subadditivity are introduced, similarly to the classical ones introduced by Lamberto Cesari. Some versions of theorems similar to the classical ones are proved. As applications, we give a comparison with the Riemann-integral and the monotone integral for Riesz space-valued functions, and we prove some relations between continuous point functions of bounded variation and quasi-additivity of corresponding set functions.