@booklet {weiss-eitofoi2006,
	title = {Entropy Is the Only Finitely Observable Invariant},
	howpublished = {Discussion Papers},
	year = {2006},
	month = {5},
	abstract = {Our main purpose is to present a very surprising new characterization of the Shannon entropy of stationary ergodic processes. We will use two basic concepts: isomorphism of stationary processes and a notion of finite observability, and we will see how one is led, inevitably, to Shannon{\textquoteright}s entropy. A function J with values in some metric space, defined on all finite-valued, stationary, ergodic processes is said to be finitely observable (FO) if there is a sequence of functions Sn(x1,x2,...,xn) that for all processes~\S converges to J(\S) for almost every realization x1{\textasciicircum}\v z of \S. It is called an invariant if it returns the same value for isomorphic processes. We show that any finitely observable invariant is necessarily a continuous function of the entropy. Several extensions of this result will also be given.},
	url = {/files/dp420.pdf},
	author = {Weiss, Donald Ornstein and Benjamin, Nathans,}
}
