On the theory of improper definite integrals

10. In this paper I wish to define a system of types of improper simple definite integrals, a system embracing in particular the four current types; of the theory of the general type I give at present merely the elements, the methods employed, however, being characteristic. The four current types are compared in ? 1 2-13o. By way of generalization of their diversities the new types arise (1lo-17o). As the desirable basis for the new types I propose (160) an extension of the notion of the proper simple definite integral; this involves likewise an extension of the notions of the four current types. In ? 2 I state in convenient notations a body of elementary properties of the general type of integrals. These properties with two definitional processes of induction developed in ?? 3, 4 serve as the basis for the definition in ? 5 of the system of types of improper integrals related to the (extended) type of proper integrals defined in 160.