Vitali Lemma approach to differentiation on a time scale

Chuan Jen Chyan; Andrzej Fryszkowski

Studia Mathematica, Tome 162 (2004), p. 161-173 / Harvested from The Polish Digital Mathematics Library

Résumé

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, $\int_{[a, b)} f ₊^{'} (x) d μ_{Δ} \leq f (b) - f (a)$ .

Publié le : 2004-01-01

Zbl 1065.26007

EUDML-ID : urn:eudml:doc:285072

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     title = {Vitali Lemma approach to differentiation on a time scale},
     journal = {Studia Mathematica},
     volume = {162},
     year = {2004},
     pages = {161-173},
     zbl = {1065.26007},
     language = {en},
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Chuan Jen Chyan; Andrzej Fryszkowski. Vitali Lemma approach to differentiation on a time scale. Studia Mathematica, Tome 162 (2004) pp. 161-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-2-4/