If we are integrating $f(x,y)$ over $R = (-\infty,\infty) \times (-\infty,\infty)$, would it be right to say:
$$\iint_{R} f(x,y) \thinspace \mathrm{d}A = \lim_{\lambda \to \infty} \displaystyle{\int_{-\lambda}^{\lambda}\left( \int_{-\lambda}^{\lambda} f(x,y)\thinspace \mathrm{d}y \right) \mathrm{d}x} = \lim_{\lambda \to \infty} \displaystyle{\int_{-\lambda}^{\lambda}\left( \int_{-\lambda}^{\lambda} f(x,y)\thinspace \mathrm{d}x \right) \mathrm{d}y} $$
(as long as $f(x,y)$ is Lebesgue integrable over $R$, Fubini's theorem applies and, provided that the limit exists)?
Or is this not good practice/does it not work all the time? Would it be better to have four different dummy variables and 4 limits?