9781461267331 - radon integrals: an abstract approach to integration and riesz representation through function cones (progress in mathematics, band 103) von anger, b.; portenier, c. (3 Ergebnisse)
Sprache: Englisch
Verlag: Birkhäuser 2012
Serie: Progress in Mathematics, Buch 16 von 170. Buch 16 von 170 - Progress in Mathematics
- Softcover
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Radon Integrals: An abstract approach to integration and Riesz representation through function cones
Sprache: Englisch
Verlag: Birkh?user 2012
Serie: Progress in Mathematics, Buch 16 von 170. Buch 16 von 170 - Progress in Mathematics
- Softcover
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Zustand: New. 2012. Paperback. . . . . . Books ship from the US and Ireland.
Sprache: Englisch
Verlag: Birkhäuser Boston 2012
Serie: Progress in Mathematics, Buch 16 von 170. Buch 16 von 170 - Progress in Mathematics
- Softcover
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, fini…te 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.
