Abstract—The notion of Cartesian net is introduced in order to provide an appropriate setting for the notion of double limit for directed functions defined on Cartesian products of spaces. As an application, we obtain extensions of the Fubini-Tonelli type theorem to the setting of the extended notion of integrability recently introduced.

Index Terms—Cartesian nets, Fubini-Tonelli theorem, vector integration.

Mangatiana A. Robdera is with Department of Mathematics, University of Botswana, 4775 Notwane Road, Gaborone, Botswana (email: robdera@yahoo.com).

Cite: Mangatiana A. Robdera, "On Cartesian Nets and Fubini-Tonelli Type Theorem," International Journal of Applied Physics and Mathematics vol. 7, no. 2, pp. 118-127, 2017.