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010   $a1-282-71436-8
010   $a9786612714368
010   $a3-11-020321-9
024 7 $a10.1515/9783110203219
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035   $a(OCoLC)651048124
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035   $a(OCoLC)840443909
035   $a(OCoLC)948655947
035   $a(DE-B1597)9783110203219
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100   $a20091012d2010      uy             0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt
182   $cc
183   $acr
200 00$aIntegral representation theory$b[electronic resource] $eapplications to convexity, banach spaces and potential theory /$fJaroslav Lukes? ... [et al.]
210   $aBerlin ;$aNew York $cWalter de Gruyter$dc2010
215   $a1 online resource (731 p.)
225 1 $aDe Gruyter studies in mathematics ;$v35
300   $aDescription based upon print version of record.
311   $a3-11-020320-0 
320   $aIncludes bibliographical references and index.
327   $t Frontmatter -- $tContents -- $t1 Prologue -- $t2 Compact convex sets -- $t3 Choquet theory of function spaces -- $t4 Affine functions on compact convex sets -- $t5 Perfect classes of functions and representation of affine functions -- $t6 Simplicial function spaces -- $t7 Choquet theory of function cones -- $t8 Choquet-like sets -- $t9 Topologies on boundaries -- $t10 Deeper results on function spaces and compact convex sets -- $t11 Continuous and measurable selectors -- $t12 Constructions of function spaces -- $t13 Function spaces in potential theory and the Dirichlet problem -- $t14 Applications -- $t Backmatter
330   $aThis monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
410  0$aDe Gruyter studies in mathematics ;$v35.
606   $aFunctional analysis
606   $aConvex domains
606   $aBanach spaces
606   $aPotential theory (Mathematics)
606   $aIntegral representations
610   $aConvex Analysis.
610   $aDirichlet Problem.
610   $aFunctional Analysis.
610   $aPartial Differential Equation.
610   $aPotential Theory.
615  0$aFunctional analysis.
615  0$aConvex domains.
615  0$aBanach spaces.
615  0$aPotential theory (Mathematics)
615  0$aIntegral representations.
676   $a515.7
686   $aSK 600$2rvk
700   $aLuke?$b Jaroslav, $059225
701   $aLukes?$b Jaroslav$f1940-$059225
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910780706903321
996   $aIntegral representation theory$93832134
997   $aUNINA