A concept of measurability for the Daniell integral
A note on Carathéodory type function
A Note on Quasicontinuous Kernels Representing Quasi-Linear Positive Maps.
A Radon-Nikodym derivative for positive linear functionals
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 remark on Edgar's extremal integral representation theorem
A representation theorem for operators on a space of interval functions.
A simple proof of the Borel extension theorem and weak compactness of operators
Let be a locally compact Hausdorff space and let be the Banach space of all complex valued continuous functions vanishing at infinity in , provided with the supremum norm. Let be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of -valued -additive Baire measures on 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 when...
A simplified proof of the Daniell integral extension theorem in ordered spaces
Absolute continuity theorems for abstract Riemann integration
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
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.
Acknowledgement of priority: Second derivates of convex functions.
Additivity of Certain Functionals and the Construction of Invariant Integrals.
An Abstract Approach to Weak Topologies in Spaces of Measures
An axiomatic approach to Quantum Gauge Field Theory
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
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.
An extension of the Steinhaus-Weil theorem
Applications p-radonifiantes et théorème de dualité