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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Radon Integrals - An abstract approach to integration and Riesz representation through function cones (Hardcover, 1992 ed.)
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Radon Integrals - An abstract approach to integration and Riesz representation through function cones (Hardcover, 1992 ed.)
Series: Progress in Mathematics, 103
Expected to ship within 18 - 22 working days
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In topological measure theory, Radon measures are the most
important objects. In the context of locally compact spaces, there
are two equivalent canonical definitions. As a set function, a
Radon measure is an inner compact regular Borel measure, finite on
compact sets. As a functional, it is simply a positive linear form,
defined on the vector lattice of continuous real-valued functions
with compact support. During the last few decades, in particular
because of the developments of modem probability theory and
mathematical physics, attention has been focussed on measures on
general topological spaces which are no longer locally compact,
e.g. spaces of continuous functions or Schwartz distributions. For
a Radon measure on an arbitrary Hausdorff space, essentially three
equivalent definitions have been proposed: As a set function, it
was defined by L. Schwartz as an inner compact regular Borel
measure which is locally bounded. G. Choquet considered it as a
strongly additive right continuous content on the lattice of
compact subsets. Following P.A. Meyer, N. Bourbaki defined a Radon
measure as a locally uniformly bounded family of compatible
positive linear forms, each defined on the vector lattice of
continuous functions on some compact subset.
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