The McShane, PU and Henstock integrals of Banach valued functions

Luisa Di Piazza; Valeria Marraffa

Displaying similar documents to “The McShane, PU and Henstock integrals of Banach valued functions”

A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals

C. K. Fong (2002)

Czechoslovak Mathematical Journal

Similarity:

We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.

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

Tuo-Yeong Lee (2005)

Mathematica Bohemica

Similarity:

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 $(x, y) \in {[0, 1]}^{2}$ .

On Henstock-Dunford and Henstock-Pettis integrals.

Ye, Guoju, An, Tianqing (2001)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions

Guoju Ye (2006)

Mathematica Bohemica

Similarity:

In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on $ℝ^{m}$ with values in a Banach space.