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On convergence of integrals in o-minimal structures on archimedean real closed fields

Tobias Kaiser (2005)

Annales Polonici Mathematici

We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.

On Denjoy-Dunford and Denjoy-Pettis integrals

José Gámez, José Mendoza (1998)

Studia Mathematica

The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function $f : [a, b] \to c_{0}$ which is not Pettis integrable on any subinterval in [a,b], while $ʃ_{J} f$ belongs to $c_{0}$ for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...

Currently displaying 261 – 280 of 542

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Displaying 261 – 280 of 542

On convergence of integrals in o-minimal structures on archimedean real closed fields

On Denjoy-Dunford and Denjoy-Pettis integrals

On extension of Baire vector measures

On extension of group valued measures

On extension of maps with values in ordered spaces

On extension of vector polymeasures

On extension of vector polymeasures. II.

On functions whose improper Riemann integral is absolutely convergent

On Henstock-Dunford and Henstock-Pettis integrals.

On homomorphisms of projective lattices in complex Hilbert spaces

On ideals with projective bases.

On integration and the Radon-Nikodym theorem in quasicomplete locally convex topological vector spaces.

On integration in Banach spaces, I

On integration in Banach spaces, III

On integration in Banach spaces, IV

On integration in Banach spaces, IX. Integration with respect to polymeasures

On integration in Banach spaces, V

On integration in Banach spaces, VI

On integration in Banach spaces, VII

On integration in Banach spaces, VIII. Polymeasures

Currently displaying 261 – 280 of 542