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Teorema de Ramsey aplicado a álgebras de Boole.

F. Benítez Trujillo (1990)

Collectanea Mathematica

Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.

The ap-Denjoy and ap-Henstock integrals

Jae Myung Park, Jae Jung Oh, Chun-Gil Park, Deuk Ho Lee (2007)

Czechoslovak Mathematical Journal

In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.

The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

Czechoslovak Mathematical Journal

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 integrable...

The divergence theorem

Josef Král (1996)

Mathematica Bohemica

This is an expository paper dealing with Jan Marik's results concerning perimeter and the divergence theorem of Gauss-Green-Ostrogradski.

The Henstock-Kurzweil approach to Young integrals with integrators in BV φ

Boonpogkrong Varayu, Tuan-Seng Chew (2006)

Mathematica Bohemica

In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral ∫ a b f d g exists if f ∈ B V φ [ a , b ] , g ∈ B V ψ [ a , b ] and ∑ n = 1 ∞ φ - 1 ( 1 / n ) ψ - 1 ( 1 / n ) < ∞ . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.

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

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.

The Kurzweil construction of an integral in ordered spaces

Beloslav Riečan, Marta Vrábelová (1998)

Czechoslovak Mathematical Journal

This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space T with respect to an ordered group valued measure are proved in this paper.

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