LDR 02618nac 22003611u 4500 010 _a0198529384 _brel. 090 _a10558 101 _aeng 102 _aUS 100 _a20091130 frey50 200 _aTopics on analysis in metric spaces _bM _fLuigi Ambrosio, Paolo Tilli 210 _aNew York _cOxford University Press _d2004 215 _a1 vol. (133 p.) _d24 225 _aOxford lecture series in mathematics and its applications _v25 _9169397 300 _aThe book is a concise introduction to analysis in metric spaces but most topics make a good foundation also for convex and fractal geometry. The exposition covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems and Sobolev spaces; all these topics are developed in a general metric setting. One chapter is devoted to the minimal connection problem. It includes both the classical problem of the existence of geodesics in finitely compact metric spaces (due to Busemann) and the abstract Steiner problem (the solution of which is based on the Gromov embedding theorem). The last chapter contains a very general description of the theory of integration with respect to a nondecreasing set of functions. The strictly presented material is enlarged by numerous remarks and also by the end-of-chapter exercises. (Zentralblatt) 320 _aBibliogr.p.125-129. Index 410 _9168310 _aOxford university press _tOxford lecture series in mathematics and its applications _v0025 676 _a2010 686 _a28B05 _9162885 _bMeasure and integration -- Set functions, measures and integrals with values in abstract spaces _xVector-valued set functions, measures and integrals _20 686 _9162882 _a28A80 _bMeasure and integration -- Classical measure theory _xFractals _20 686 _9162881 _a28A78 _bMeasure and integration -- Classical measure theory _xHausdorff and packing measures _20 686 _9162939 _a30C65 _bFunctions of a complex variable -- Geometric function theory _xQuasiconformal mappings in Rn, other generalizations _20 686 _a31C15 _9163038 _bPotential theory -- Other generalizations _xPotentials and capacities _20 700 _9176030 _aAmbrosio _bLuigi _f1963- _4070 701 _4070 _aTilli _bPaolo _9176031 856 _uhttp://zbmath.org/?q=an:1080.28001 _zZentralblatt 856 _uhttp://www.ams.org/mathscinet-getitem?mr=2039660 _zMathSciNet 905 _aaw _b2005 906 _aaw _b2011-05-31 906 _aaw _b2012-11-29 995 _f02834-02 _xachat _914720 _cCMI _20 _k28 AMB _o0 _eSalle R _bCMI 995 _f02834-01 _xachat _914719 _cCMI _20 _k28 AMB _o0 _eSalle R _bCMI 001 10558