Displaying similar documents to “Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions”

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 ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .

Adjoint classes of functions in the H 1 sense

Piotr Sworowski (2007)

Czechoslovak Mathematical Journal

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Using the concept of the H 1 -integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.

The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)

Czechoslovak Mathematical Journal

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In this paper we prove an existence theorem for the Cauchy problem x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I α = [ 0 , α ] using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness.