Originally published in 1981, this excellent treatment of the mathematical theory of entropy gives an accessible exposition of the ways in which this idea has been applied to information theory, ergodic theory, topological dynamics and statistical mechanics. Scientists who want a quick understanding of how entropy is applied in disciplines not their own, or simply desire a better understanding of the mathematical foundation of the entropy function will find this to be a valuable book.

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An easily checked sufficient condition is given for the restriction of a finite Blaschke product to the unit circle to be an exact endomorphism. A formula for the entropy of such restrictions with respect to the unique finite invariant measure equivalent to Lebesgue measure is given and it is shown that if such a restriction has maximal entropy then it is conformally equivalent to the product of a rotation and a power.

[3] introduced the concept of a set inexhaustibly approaching a point. This was generalized by Cargal [4] and Block and Cargal [1] to a point which is , approached by a set. These ideas appear very closely connected with limit points of a set. In this paper we shall attempt to set these approach properties in a topological setting so that if x is "approached" by a set, it will be a limit point of this set in an appropriate topology.

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