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A Radon-Nikodym derivative for positive linear functionals

E. de Amo, M. Díaz Carrillo (2009)

Studia Mathematica

An exact Radon-Nikodym derivative is obtained for a pair (I,J) of positive linear functionals, with J absolutely continuous with respect to I, using a notion of exhaustion of I on elements of a function algebra lattice.

A simple proof of the Borel extension theorem and weak compactness of operators

Ivan Dobrakov, Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

Let T be a locally compact Hausdorff space and let C 0 ( T ) be the Banach space of all complex valued continuous functions vanishing at infinity in T , provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X -valued σ -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u C 0 ( T ) X when...

Absolute continuity theorems for abstract Riemann integration

E. de Amo, R. del Campo, M. Díaz Carillo (2007)

Czechoslovak Mathematical Journal

Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures and measures induced by integrals. To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we deal with the possibility of preserving absolute continuity when extending the elemental...

Abstract Riemann integrability and measurability

E. de Amo, R. del Campo, M. Díaz Carrillo (2009)

Czechoslovak Mathematical Journal

We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.

An axiomatic approach to Quantum Gauge Field Theory

Thomas Thiemann (1997)

Banach Center Publications

In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality...

An exact functional Radon-Nikodym theorem for Daniell integrals

E. de Amo, I. Chitescu, M. Díaz Carrillo (2001)

Studia Mathematica

Given two positive Daniell integrals I and J, with J absolutely continuous with respect to I, we find sufficient conditions in order to obtain an exact Radon-Nikodym derivative f of J with respect to I. The procedure of obtaining f is constructive.

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