Sampling Theorem:

Let $ x(t)\ $ be a BAND-LIMITED signal with $ X(\omega) = 0\ $ for $ |\omega| > \omega_m\ $. Then $ x(t)\ $ is uniquely determined by its samples $ x(nT)\ $, n=-2,-1,0,1,2... IF $ \omega_s > 2\omega_m\ $, where $ \omega_x = 2 \frac{\pi}{T} $.

Given these samples, we can reconstruct $ x(t)\ $ through an impulse train where amplitudes are successive sample values.

THIS DEFINITION IS EXTRACTED FROM THE TEXTBOOK.

Signals & Systems Second Edition Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab