Vitali Lemma approach to differentiation on a time scale

Tom 162 / 2004

Chuan Jen Chyan, Andrzej Fryszkowski Studia Mathematica 162 (2004), 161-173 MSC: Primary 26A24, 28A15; Secondary 46G05, 39A05, 28A05. DOI: 10.4064/sm162-2-4

Streszczenie

A new approach to differentiation on a time scale ${{\mathbb T}}$ is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function $f:{{\mathbb T}}\rightarrow {\mathbb R}$ has a right derivative $f_{+}^{\prime } ( x) $ for $\mu _{\Delta } $-almost all $x\in {{\mathbb T}}$. Moreover, $\int _{[ a,b) }f_{+}^{\prime } ( x) \kern .16667em d\mu _{\Delta }\leq f ( b) -f ( a) .$

Autorzy

  • Chuan Jen ChyanDepartment of Mathematics
    Tamkang University
    Taipei 251, Taiwan
    e-mail
  • Andrzej FryszkowskiFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail

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