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Start Over Creator Di Piazza, Luisa

1. Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions

Creator:
Bongiorno, B., Di Piazza, Luisa, and Musiał, Kazimierz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil-Henstock integral, Kurzweil-Henstock-Pettis integral, and Pettis integral
Language:
English
Description:
We study the integrability of Banach valued strongly measurable functions defined on [0, 1]. In case of functions f given by ∞∑ n=1 xnχEn , where xn belong to a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for the Bochner and for the Pettis integrability of f (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
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

4. Variational measures related to local systems and the Ward property of $\scr P$-adic path bases

Creator:
Bongiorno, Donatella , Di Piazza, Luisa, and Skvortsov, Valentin A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
local system, ${\mathcal{P}}$-adic system, differentiation basis, variational measure, and Ward property
Language:
English
Description:
Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a $\mathcal{P}$-adic path system that defines a differentiation basis which does not possess Ward property.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public