A theorem that says that Band-limited functions only need to be sampled on a discrete set of points (finite if the function has bounded support) to be reconstructed exactly! This is because the space of band-limited functions is spanned by the set of Sinc functions translated by discrete amounts (the amount depending on the max freq of the band-limited funs, as here).
The basis of analog to digital conversion
This also is related to the Discrete Fourier transform