Integration by Parts
Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions
We study the integrability of Banach valued strongly measurable functions defined on . In case of functions given by , where belong to a Banach space and the sets are Lebesgue measurable and pairwise disjoint subsets of , there are well known characterizations for the Bochner and for the Pettis integrability of (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
Kurzweil’s PU integral as the Lebesgue integral
For a merely continuous partition of unity the PU integral is the Lebesgue integral.
La substitution dans les intégrales de Riemann-Stieltjes
Lebesgue's Convergence Theorem of Complex-Valued Function
In this article, we formalized Lebesgue's Convergence theorem of complex-valued function. We proved Lebesgue's Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue's Convergence Theorem of complex-valued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences and showed their...
Lebesgueův integrál v abstraktních prostorech
Linear integral equations in the space of regulated functions.
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Linear Stieltjes integral equations in Banach spaces
Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in [5]. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. [3]). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the basis of...
Lokale Integralnomen und verallgemeinerte uneigentliche Riemann-Stieltjes-Integrale.
Mémoire sur les fonctions discontinues
Mémoire sur les intégrales définies, prises entre des limites imaginaires
Monotone and convex -algebra valued functions.
Multidimensional extension of L. C. Young's inequality.
Nonabsolutely convergent series
Assume that for any from an interval a real number is given. Summarizing all these numbers is no problem in case of an absolutely convergent series . The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral.
Nonstandard analysis and generalized Riemann integrals
Note sur une formule de calcul intégral
Nouvelles applications des fractions continues
O hmotě trojosého ellipsoidu
O integrování racionálných differenciálů