Real integrable spaces

M. Wilhelm

Displaying similar documents to “Real integrable spaces”

The Denjoy extension of the Bochner, Pettis, and Dunford integrals

R. Gordon (1989)

Studia Mathematica

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The McShane, PU and Henstock integrals of Banach valued functions

Luisa Di Piazza, Valeria Marraffa (2002)

Czechoslovak Mathematical Journal

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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...

On Henstock-Dunford and Henstock-Pettis integrals.

Ye, Guoju, An, Tianqing (2001)

International Journal of Mathematics and Mathematical Sciences

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On Denjoy-Dunford and Denjoy-Pettis integrals

José Gámez, José Mendoza (1998)

Studia Mathematica

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The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function $f : [a, b] \to c_{0}$ which is not Pettis integrable on any subinterval in [a,b], while $ʃ_{J} f$ belongs to $c_{0}$ for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with...

The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

Czechoslovak Mathematical Journal

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In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval $[a, b]$ into a Banach space $X .$ It is shown that a Denjoy-Bochner integrable function on $[a, b]$ is Denjoy-Riemann integrable on $[a, b]$ , that a Denjoy-Riemann integrable function on $[a, b]$ is Denjoy-McShane integrable on $[a, b]$ and that a Denjoy-McShane integrable function on $[a, b]$ is Denjoy-Pettis integrable on $[a, b] .$ In addition, it is shown that for spaces that do not contain a copy of $c_{0}$ , a measurable Denjoy-McShane...

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$ -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f {[0, 1]}^{2} ⟶ ℝ$ and a continuous function $F {[0, 1]}^{2} ⟶ ℝ$ such that $(¶) \int_{0}^{x} \{(¶) \int_{0}^{y} f (u, v) d v\} d u = (¶) \int_{0}^{y} \{(¶) \int_{0}^{x} f (u, v) d u\} d v = F (x, y)$ for all $(x, y) \in {[0, 1]}^{2}$ .

Characterizations of Kurzweil-Henstock-Pettis integrable functions

L. Di Piazza, K. Musiał (2006)

Studia Mathematica

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We prove that several results of Talagrand proved for the Pettis integral also hold for the Kurzweil-Henstock-Pettis integral. In particular the Kurzweil-Henstock-Pettis integrability can be characterized by cores of the functions and by properties of suitable operators defined by integrands.