Why does $$\left(\int_{-\infty}^{\infty}e^{-t^2}dt\right)^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2 + y^2)}dx\,dy ?$$
This came up while studying Fourier analysis. What's the underlying theorem?
Why does $$\left(\int_{-\infty}^{\infty}e^{-t^2}dt\right)^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2 + y^2)}dx\,dy ?$$
This came up while studying Fourier analysis. What's the underlying theorem?
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