In 1949, Claude Elwood Shannon and Warren Weaver wrote The Mathematical Theory of Communication. (ISBN 0252725484) This founded the modern discipline of information theory. Thus it is possible to measure the amount of information in a message.

Shannon's law

where
C = bits per second - channel capacity,
W = frequency - bandwidth,
S/N = signal-to-noise ratio,
shows that there is a theoretical maximum amount of information that can be transmitted over a bandwidth-limited carrier in the ever-present background noise.