Question is that

Define a functionon the unit square[0,1][0,1]by

f( x , y ) = 1 if x = rational ay if x = irrationalNote that f(x, y) = 2y almost everywhere in [0, 1] , because the set of discontinuities has measure zero: M((Q n [0, 1]) x [0, 1]) = M(Q n [0, 1]) . M([0, 1]) = 0 . (1 - 0) = 0. Therefore, we immediately deduce that f(x, y) dA = 2ydx dy = 1 [0, 1]2 0 215 views . View 13 upvotes