Wolfgang Sander

Characterizations of information measures

The branching property recursivity properties the fundamental equation of information and regular recursive measures sum form information measures and additivity properties sum form information measures additive sum form information measures additive sum form information measures of type 1 additive sum form information measures of multiplicative type.

On measures of fuzziness

Abstract We present a characterization of a fuzzy entropy which is formally analogous to the information theoretical Shannon entropy.

Verallgemeinerungen eines Satzes von S. Piccard

The following result is due to S. Piccard ([12], S.30): “If A,B ⊂ℝ are Baire sets of second category and if the function f: ℝ×ℝ→ℝ is defined by f(x,y):=x−y (x,y ε ℝ), then the interior of f(A×B) is non void”. In this note the two main results assure, that the theorem of S. Piccard remains valid, if (1) ℝ is replaced by topological spaces X,Y,Z, (2) f:X×Y→Z is a function, which satisfies a certain global (respectively local) solvability condition, (3) A ⊂X contains a Baire set of second category and (4) B ⊂Y is only of second category.

Verallgemeinerungen eines Satzes von H. Steinhaus

The following result is due to H. Steinhaus [20]: “If A,B⊂R are sets of positive inner Lebesgue measure and if the function f: R x R→R is defined by f(x,y):=x+y (x,yɛR), then the interior of f(A x B) is non void”. In this note there is proved, that the theorem of H. Steinhaus remains valid, if(1)R is replaced by certain topological measure spaces X, Y and a Hausdorff space Z,(2)f is a continuous function from an open set T⊂X x Y into Z and satisfies a special local (respectively global) solvability condition in T,(3)A⊂X is a set of positive outer measure, B⊂Y contains a set of positive measure and A x B⊂T.

Characterizations of sum form information measures on open domains

SummaryThe goal of this paper is to give a survey of all important characterizations of sum form information measures that depend uponk discrete complete probability distributions (without zero probabilities) of lengthn and which satisfy a generalized additivity property. It turns out that most of the problems have been solved, but some open problems lead to the very simple looking functional equations

Ein Beitrag zur Baire-Kategorie-Theorie

f(pq) + f(p(1 - q)) + f((1 - p)q) - f((1 - p)(1 - q)) = 0, p,q \in ]0, 1[^k (FE)

General Solution of Two Functional Equations Concerning Measures of Information

and