A step to Kurzweil-Henstock—an outline

B. D. Craven

Displaying similar documents to “A step to Kurzweil-Henstock—an outline”

Bounded linear functionals on the space of Henstock-Kurzweil integrable functions

Tuo-Yeong Lee (2009)

Czechoslovak Mathematical Journal

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Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.

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

A scalar Volterra derivative for the PoU-integral

V. Marraffa (2005)

Mathematica Bohemica

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A weak form of the Henstock Lemma for the $P o U$ -integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the $P o U$ -integral. Also the $P o U$ -integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.