Great post! Helped me build an intuition of why this is true, and I came off pretty convinced it is.
I specially liked how each step is well motivated, so that by the end I already knew where this was going.
One note:
In the last section you write that the convolution of the distribution equals the Fourier transform of the pointwise distributions.
But I think you meant to write that the Fourier transform of the convolution of the distributions is the pointwise product of their Fourier transforms (?).
Great post! Helped me build an intuition of why this is true, and I came off pretty convinced it is.
I specially liked how each step is well motivated, so that by the end I already knew where this was going.
One note:
In the last section you write that the convolution of the distribution equals the Fourier transform of the pointwise distributions.
But I think you meant to write that the Fourier transform of the convolution of the distributions is the pointwise product of their Fourier transforms (?).
This does not break the proof.
Appreciate it! And you’re right, that was a mistake in the last section—just fixed it. Thanks!