Multiple Lebesgue integration on time scales
نویسندگان
چکیده
منابع مشابه
Multiple Lebesgue Integration on Time Scales
Differential and integral calculus on time scales allows to develop a theory of dynamic equations in order to unify and extend the usual differential equations and difference equations. For single variable differential and integral calculus on time scales, we refer the reader to the textbooks [4, 5] and the references given therein. Multivariable calculus on time scales was developed by the aut...
متن کاملNotes on Lebesgue Integration
These notes record the lectures on Lebesgue integration, which is a topic not covered in the textbook. It is largely inspired by the approach of Leon Simon when he previously taught this course. (All mistakes are my own of course!) The notes will be posted after each lecture. Any comments or corrections, even very minor ones, are very much appreciated! Our goal is to define the notion of Lebesg...
متن کاملExpression of the Lebesgue ∆-integral on time scales as a usual Lebesgue integral; application to the calculus of ∆-antiderivatives
The theory of dynamic equations appears in the literature in 1988 in the Ph. D. of S. Hilger [18]. The aim of this theory consists in to study differential and difference equations under the same formulation. Thus, the concepts of ∆– derivative and ∆−integral have been defined. These two concepts cover both the classical derivative and the Riemann integral together with the forward and sum oper...
متن کاملCell water dynamics on multiple time scales.
Water-biomolecule interactions have been extensively studied in dilute solutions, crystals, and rehydrated powders, but none of these model systems may capture the behavior of water in the highly organized intracellular milieu. Because of the experimental difficulty of selectively probing the structure and dynamics of water in intact cells, radically different views about the properties of cell...
متن کاملCovering theorems and Lebesgue integration
Abstract. This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let X be a finite dimensional normed space; let μ be a Radon measure on X and let Ω ⊆ X be a μ-measurable set. For λ ≥ 1, a μ-measurable set Sλ(a) ⊆ X is a λ-Morse set with tag a ∈ Sλ(a) if there is r > 0 such that B(a, r) ⊆ Sλ(a) ⊆ B(a, λr)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2006
ISSN: 1687-1839,1687-1847
DOI: 10.1155/ade/2006/26391