Measurability of functions of two variables
J. H. Michael, Basil C. Rennie · Journal of the Australian Mathematical Society · 1959
Summary This paper investigates the existence and equality of the double and repeated integrals of a real function on a plane set. The main result (Theorem 2) is that if a function on a plane Lebesgue measurable set is continuous in one variable and measurable in the other then it is measurable in the plane.