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A note on measures on time scales

100%

Rzeżuchowski T.

Demonstratio Mathematica

2005

tom Vol. 38, nr 1

79--84

A connection between the measures used on time scales and usual Lebesgue measure is established and applied to simple justifications of some recently published results on Vitali covering theorem and (delta)-differentiability of monotone functions defined on time scales.

Niektóre zagadnienia dotyczące nauczania matematyki na kierunku Budownictwo

100%

Rzeżuchowski T.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Budownictwo

2005

tom Z. 45

333-337

Autonomous differential inclusion sharing the families of trajectories

63%

Leśniewski A. , Rzeżuchowski T.

Demonstratio Mathematica

2006

tom Vol. 39, nr 2

347-356

We give a sufficient condition for equality of sets of trajectories of two differential inclusions with right-hand sides Borel measurable with respect to the state variable, not necessarily bounded and possibly containing the origin.

The completion of the space of convex, bounded sets with respect to the Demyanov metric

51%

Grzybowski J. , Leśniewski A. , Rzeżuchowski T.

Demonstratio Mathematica

2013

tom Vol. 46, nr 1

191--196

The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.