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001 978-3-540-48719-7
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007 cr nn 008mamaa
008 121227s2001 gw | s |||| 0|eng d
020 _a9783540487197
_9978-3-540-48719-7
024 7 _a10.1007/b76887
_2doi
050 4 _aQA404.7-405
072 7 _aPBWL
_2bicssc
072 7 _aMAT033000
_2bisacsh
072 7 _aPBWL
_2thema
082 0 4 _a515.96
_223
245 1 0 _aLectures on Choquet’s Theorem
_h[electronic resource] /
_cedited by Robert R. Phelps.
250 _aSecond Edition.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2001.
300 _aX, 130 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1757
505 0 _aThe Krein-Milman theorem as an integral representation theorem -- Application of the Krein-Milman theorem to completely monotonic functions -- Choquet’s theorem: The metrizable case. -- The Choquet-Bishop-de Leeuw existence theorem -- Applications to Rainwater’s and Haydon’s theorems -- A new setting: The Choquet boundary -- Applications of the Choquet boundary to resolvents -- The Choquet boundary for uniform algebras -- The Choquet boundary and approximation theory -- Uniqueness of representing measures. -- Properties of the resultant map -- Application to invariant and ergodic measures -- A method for extending the representation theorems: Caps -- A different method for extending the representation theorems -- Orderings and dilations of measures -- Additional Topics.
520 _aA well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.
650 0 _aPotential theory (Mathematics).
650 0 _aFunctional analysis.
650 1 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
700 1 _aPhelps, Robert R.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662173381
776 0 8 _iPrinted edition:
_z9783540418344
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1757
856 4 0 _uhttps://doi.org/10.1007/b76887
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12280
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