Integration and measurability
The author discusses the part of the traditional requirement of measurability of the integrand function \(f\) and the set \(A\) with respect to which the integration is carried out in the theory of integration. A modification of the integral definition is presented where the requirement of measurability of \(A\) and \(f\) is absent. Besides, it is shown that some properties of the Lebesgue integral are preserved.
scientific article; zbMATH DE number 1261637