Vitali Lemma approach to differentiation on a time scale

• Autorzy: Chuan Jen Chyan , Andrzej Fryszkowski
• Języki publikacji: EN

Abstrakty

EN

A new approach to differentiation on a time scale 𝕋 is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: 𝕋 → ℝ has a right derivative f₊'(x) for $μ_{Δ}$-almost all x ∈ 𝕋. Moreover, $∫_{[a,b)} f₊'(x)dμ_{Δ} ≤ f(b) - f(a)$.

Kategorie tematyczne

• 39A05: General theory
• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 46G05: Derivatives
• 28A15: Abstract differentiation theory, differentiation of set functions
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 2
• Strony: 161-173

Daty

wydano

2004

Twórcy

autor

Chuan Jen Chyan

• Department of Mathematics, Tamkang University, Taipei 251, Taiwan

autor

Andrzej Fryszkowski

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm162-2-4