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2012•Journal of Informatics and Mathematical SciencesOpen access

Extensions of Lattice Set Functions to Regular Borel Measures

P. Maritz

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Abstract

This paper deals with the unique extension of a finite regular set function from the $\delta$-lattice of all compact $G_\delta$-subsets of a locally compact Hausdorff space to a finite regular measure on the $\delta$-ring of all relatively compact Borel subsets of the space. This extension is a two-step method because it is performed (without density assumptions) via the $\delta$-ring of all relatively compact Baire subsets of the space.

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What this paper is about

This paper deals with the unique extension of a finite regular set function from the $\delta$-lattice of all compact $G_\delta$-subsets of a locally compact Hausdorff space to a finite regular measure on the $\delta$-ring of all relatively compact Borel subsets of the space. This extension is a two-step method because it is performed (without density assumptions) via the $\delta$-ring of all relatively compact Baire subsets of the space.

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Available abstract

This paper deals with the unique extension of a finite regular set function from the $\delta$-lattice of all compact $G_\delta$-subsets of a locally compact Hausdorff space to a finite regular measure on the $\delta$-ring of all relatively compact Borel subsets of the space. This extension is a two-step method because it is performed (without density assumptions) via the $\delta$-ring of all relatively compact Baire subsets of the space.

Key concepts: Riesz–Markov–Kakutani representation theorem, Mathematics, Borel measure, Locally compact space, Extension (predicate logic), Hausdorff space, Compact space, Continuous functions on a compact Hausdorff space

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