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Start Over Creator Marraffa, Valeria

1. Riemann type integrals for functions taking values in a locally convex space

Creator:
Marraffa, Valeria
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Pettis integral, McShane integral, Kurzweil-Henstock integral, and locally convex spaces
Language:
English
Description:
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The McShane, PU and Henstock integrals of Banach valued functions

Creator:
Di Piazza, Luisa and Marraffa, Valeria
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Pettis, McShane, PU and Henstock integrals, variational integrals, and multipliers
Language:
English
Description:
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Variational Henstock integrability of Banach space valued functions

Creator:
Di Piazza, Luisa, Marraffa, Valeria, and Musiał, Kazimierz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil-Henstock integral, variational Henstock integral, and Pettis integral
Language:
English
Description:
We study the integrability of Banach space valued strongly measurable functions defined on [0, 1]. In the case of functions f given by ∑ ∞ n=1 xnχEn , where xn are points of a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for Bochner and Pettis integrability of f. The function f is Bochner integrable if and only if the series ∑∞ n=1 xn|En| is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of f. In this paper we give some conditions for variational Henstock integrability of a certain class of such functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public