regarding the theoretical definition of double integrals, is it correct to think of them as a kind of double Riemann sums, sums of 2d planes? sometimes the order of integration results in simplification of the calculuation....

once you have mastered Lebegue Integration and measure theory is Fubini's theorem and Riemann integration not useful...

I(limit a to b) I(limit c to d) f(x,y)dydx= I (limit c to d) I (limit a to b) f(x,y)dxdy

thanks very much!