An approach of the theory of integration by the mean of biased test functions (Q1282234)

Written in the framework of nonstandard analysis (relative set theory), the authors generalize earlier contributions of Loos from one-dimensional to multidimensional integrals on a product of intervals. The compact and non-compact cases are considered. In the compact case, the obtained integral is equivalent to the Lebesgue integral. In the non-compact case, the proposed integral is some type of improper integral. It is not necessarily additive.