On composition of functions and measures

• Autorzy: Ryszard Rudnicki

Abstrakty

EN

 Abstract: Let μ be a vector measure with values in $ℝ^k$ and $f:ℝ^k → ℝ$. A measure ν is called the composition of f and μ if for every δ-sequence $(δ_n)$ the sequence $f(μ*δ_n)$ is weakly convergent to ν. We give sufficient conditions for the existence of the composition and examples of geometric applications.

Słowa kluczowe

EN

measure; δ-sequence; composition

Kategorie tematyczne

• 28B05: Vector-valued set functions, measures and integrals
• 28A33: Spaces of measures, convergence of measures

Twórcy

autor

Ryszard Rudnicki

• Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland
• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

• Książka: Different aspects of differentiability

Bibliografia

[1] P. Antosik, J. Mikusiński and R. Sikorski, Theory of Distributions, The Sequential Approach, Elsevier and PWN, Amsterdam-Warszawa, 1973.
[2] P. Antosik, On composition of distributions, Proc. Steklov Math. Inst., to appear.
[3] N. Bourbaki, Éléments de mathématiques, Livre VI, Intégration, Hermann, Paris, 1956.
[4] S. Łojasiewicz, An Introduction to the Theory of Real Functions, (A. V. Ferreira, ed.), Wiley, Chichester, 1989.

• Kolekcja: DML-PL