Kurzweil-stieltjes Integral: Theory And Applications
World Scientific, 26. 9. 2018 - Počet stran: 400
The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.
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a e a,b absolutely convergent assume ATA(t Banach space bounded variation Cauchy condition Consequently Consider continuous linear functional convergence theorem Corollary countable defined Definition denoted dg eacists edp(t Exercise exists and equals exponential function f dg exists finite step function formula function f functions of bounded gauge given Hence implies inequality integrable with respect integral ſ integral ſº f intentionally left blank interval a,b Krejc´ı Kurzweil Kurzweil-Stieltjes integral Lebesgue-Stieltjes integral left-continuous Lemma Let f matrix Monteiro Moreover nondecreasing nonnegative oj_1 outer measure partition of a,b proof is complete prove regulated functions Remark respect to g Riemann integral Riemann-Stieltjes integral satisfies ſaw Schwabik sequence ſº f dg ſoj_1 Stieltjes integral subinterval t e a,b tion Tvrdý uniformly convergent uniformly integrable unique solution V-integrals var(f varº