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On the Kluvánek Construction of the Lebesgue Integral

Beloslav Riečan — 2013

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

I. Kluvánek suggested to built the Lebesgue integral on a compact interval in the real line by the help of the length of intervals only. In the paper a modification of the Kluvánek construction is presented applicable to abstract spaces, too.

On the entropy and generators of dynamical systems

Beloslav Riečan — 1996

Applications of Mathematics

Recently D. Dumitrescu ([4], [5]) introduced a new kind of entropy of dynamical systems using fuzzy partitions ([1], [6]) instead of usual partitions (see also [7], [11], [12]). In this article a representation theorem is proved expressing the entropy of the dynamical system by the entropy of a generating partition.

On mean value in F -quantum spaces

Beloslav Riečan — 1990

Aplikace matematiky

The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.

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