On entropy-like functionals and codes for metrized probability spaces. I.
Miroslav Katětov · Czech digital mathematics library · 1990
By means of a suitable modification of the concept of code, we introduce certain entropy-like functionals on the class 20 of semimetric spaces equipped with a bounded measure.For finite spaces P G 2B, (1) we prove that these functionals can be characterized in terms not involving codes, (2) we establish some analogues of the well-known connection between the Shannon entropy of a finite probability space P and the average length of the "best" code for P n , n -• oo.