Please help me answer the following questions about area under a curve and lebesgue measure.

Corollary 15.14 (Integral as the area under a graph). Let (X, M, u) be a o-finite measure space, and give R the Borel o-algebra BR and Lebesgue measure m (restricted to BR). An unsigned function f : X -+ [0, too) is measurable if and only if the set Gf : = { ( x, t ) E X x R : 0