Vitali Lemma approach to differentiation on a time scale

Chuan Jen Chyan, and Andrzej Fryszkowski. "Vitali Lemma approach to differentiation on a time scale." Studia Mathematica 162.2 (2004): 161-173. <http://eudml.org/doc/285072>.

@article{ChuanJenChyan2004,
abstract = {A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for $μ_\{Δ\}$-almost all x ∈ . Moreover, $∫_\{[a,b)\} f₊^\{\prime \}(x)dμ_\{Δ\} ≤ f(b) - f(a)$.},
author = {Chuan Jen Chyan, Andrzej Fryszkowski},
journal = {Studia Mathematica},
keywords = {Vitali lemma; time scale; differentiation; increasing function},
language = {eng},
number = {2},
pages = {161-173},
title = {Vitali Lemma approach to differentiation on a time scale},
url = {http://eudml.org/doc/285072},
volume = {162},
year = {2004},
}

TY - JOUR
AU - Chuan Jen Chyan
AU - Andrzej Fryszkowski
TI - Vitali Lemma approach to differentiation on a time scale
JO - Studia Mathematica
PY - 2004
VL - 162
IS - 2
SP - 161
EP - 173
AB - A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for $μ_{Δ}$-almost all x ∈ . Moreover, $∫_{[a,b)} f₊^{\prime }(x)dμ_{Δ} ≤ f(b) - f(a)$.
LA - eng
KW - Vitali lemma; time scale; differentiation; increasing function
UR - http://eudml.org/doc/285072
ER -