Search results for " Integra"
showing 10 items of 2527 documents
Decomposability in the space of HKP-integrable functions
2014
In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.
A decomposition of Denjoy-Khintchine-Pettis and Henstock-Kurzweil-Pettis integrable multifunctions
2010
We proved in one of our earlier papers that in case of separable Banach space valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selector and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Moreover we show that an analogous result holds true also for the Denjoy-Khintchine-Pettis integrable multifunctions. Applying the representation theorem we describe the multipliers of HKP and DKP integrable functions. Then we use this description to obtain an operator characterization of HKP and DKP integrability.
Representation of quasi-measure by a Henstock-Kurzweil type integral on a compact zero-dimensional metric space
2009
A derivation basis is introduced in a compact zero-dimensional metric space X. A Henstock-Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on X.
MR2741185 Talvila, Erik The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219. (Reviewer: Luisa Di Piazza) 46G12 (26A39 46E…
2010
Talvila Erik, The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219, 46Gxx (26A39 46Exx) MR 2 741 185 A descriptive definition of an integral is a definition which provides a ``description'' of the space of primitives. The derivatives in some sense of the primitives are the integrands. In this paper the author introduces a descriptive method of integrating distributions: the regulated primitive integral. The set $\textbf{B}_R= \{F: [-\infty,\infty] \rightarrow {\bf R} \ \ | \mbox{ F {\it is regulated and left continuous on }}\\ \ \ {\bf R}, \ \ F(-\infty)=0, \ \ F(\infty)\in {\bf R}\}$ is the family of primitives. The derivative here is in the sense of the distribu…
A Riemann sums method in the Theory of vector Integration
2010
Relaxation result for differential inclusions with Stieltjes derivative
2023
The aim of this paper is to provide a Filippov-Wa\.{z}ewski Relaxation Theorem for the very general setting of Stieltjes differential inclusions. New relaxation results can be deduced for generalized differential problems, for impulsive differential inclusions with multivalued impulsive maps and possibly countable impulsive moments and also for dynamic inclusions on time scales.
MR2677289 Takakura, Mayumi Noncommutative integration in partial O∗-algebras. Fukuoka Univ. Sci. Rep. 40 (2010), no. 1, 1–20. (Reviewer: Francesco Ts…
2011
The Henstock-Kurzweil-Stieltjes type integral for real functions on a fractal subset of the real line
2011
The aim of this paper is to introduce an Henstock-Kurzweil type integration process for real functions on a fractal subset E of the real line.