Stochastic processes in nuclear spaces: quasi-martingales and decompositions
Strict topologies as topological algebras
Let be a completely regular Hausdorff space, the space of all scalar-valued bounded continuous functions on with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally -convex.
Strongly additive functions on lattices
Structural properties of Banach and Fréchet spaces determined by the range of vector measures.
Substitution formulas for the Kurzweil and Henstock vector integrals
Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and prove Substitution...
Sur les mesures vectorielles définies par une application Pettis-intégrable
Sur l'intégrabilité de Pettis.
Teorema de existencia y representación integral del producto tensorial de medidas vectoriales
Teorema de Ramsey aplicado a álgebras de Boole.
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 absolute continuity of functions defined on the -ring generated by a ring
The ap-Denjoy and ap-Henstock integrals
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 Bochner and the monotone integrals with respect to a nuclear-valued finitely additive measure
The Brooks-Jewett theorem for -triangular functions on difference posets and orthoalgebras
The Denjoy extension of the Bochner, Pettis, and Dunford integrals
The Denjoy extension of the Riemann and McShane integrals
In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval into a Banach space It is shown that a Denjoy-Bochner integrable function on is Denjoy-Riemann integrable on , that a Denjoy-Riemann integrable function on is Denjoy-McShane integrable on and that a Denjoy-McShane integrable function on is Denjoy-Pettis integrable on In addition, it is shown that for spaces that do not contain a copy of , a measurable Denjoy-McShane integrable...
The Fubini Theorem and Convolution of Vector-Valued Measures
The general Fubini theorem in complete bornological locally convex spaces.
The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem
In this paper we prove an existence theorem for the Cauchy problem using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function satisfies some conditions expressed in terms of measures of weak noncompactness.
The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces.
The Laplace transform of exponentially bounded vector-valued functions (real conditions)