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3 Bulletin of the Polish Academy of Sciences. Mathematics

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On a dimension of measures

Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

221-235

Using the notion of the Levy concentration function we discuss a definition of the dimension for probability measures. This dimension is strongly connected with the correlation dimension of measures and with the Hausdorff dimension of sets. Moreover, we calculate some bounds of this dimension for measures generated by Iterated Function Systems and by a partial differential equation.

Attractors of multifunetions

Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

319-334

We introduce the notion of a semiattractor and attractor for multifunctions and we show that they have properties similar to semifractals and fractals. Further we show a relationship between the multifunctions and transition functions appearing in the theory of Markov operators.

Semifractals on Polish spaces

Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

179-196

We extend the theory of semifractals to arbitrary metric spaces. We also show kow to construct semifractals on Polish spaces by a use of Markov operators and Markov chain.