For 10 points, name this quantity, often measured in bits, that names a field of mathematics begun by Claude Shannon.
Applying the ergodic theorem to a field of mathematics named for this quantity allows various scientists to develop coding theorems. That field of applied mathematics named for this quantity considers such models as additive white Gaussian noise. That field of mathematics named for this quantity was developed following the publication of the paper A Mathematical Theory of Communication. Its name comes from a 1928 Ralph Hartley paper that defines it as the number of (*) symbols in a transmission times the log of the number of possible symbols. If p-sub-i is the probability that the i•th symbol occurs, the sum for all i of p-sub-i log 2 p-sub-i is the entropy, or how much of this quantity is contained in a message. For 10 points, name this quantity, often measured in bits, that names a field of mathematics begun by Claude Shannon.
Applying the ergodic theorem to a field of mathematics named for this quantity allows various scientists to develop coding theorems.
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