If a function f(x) contains no frequencies higher than B hertz, then it can be completely determined from its ordinates at a sequence of points spaced less than 1/2B seconds apart. (Wikipedia)
That is, a continuous function can be digitally sampled and reconstructed losslessly if the sampling rate is high enough.
This is the source of the de facto standard 44.1 kHz audio sampling rate, which allows lossless capture of frequencies up to approximately 20 kHz, which is the limit of human hearing.
Often called the Nyquist-Shannon sampling theorem, but there are other claimants (Borel, Raabe, Whittaker, Kotel'nikov, Someya, Weston)