LDR 02618nac  22003611u 4500
010    _a0198529384
090    _a10558
101    _aeng
102    _aUS
100    _a20091130              frey50       
200    _aTopics on analysis in metric spaces
       _fLuigi Ambrosio, Paolo Tilli
210    _aNew York
       _cOxford University Press
215    _a1 vol. (133 p.)
225    _aOxford lecture series in mathematics and its applications
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
676    _a2010
686    _a28B05
       _bMeasure and integration -- Set functions, measures and integrals with values in abstract spaces
       _xVector-valued set functions, measures and integrals
686    _9162882
       _bMeasure and integration -- Classical measure theory
686    _9162881
       _bMeasure and integration -- Classical measure theory
       _xHausdorff and packing measures
686    _9162939
       _bFunctions of a complex variable -- Geometric function theory
       _xQuasiconformal mappings in Rn, other generalizations
686    _a31C15
       _bPotential theory -- Other generalizations
       _xPotentials and capacities
700    _9176030
701    _4070
856    _uhttp://zbmath.org/?q=an:1080.28001
856    _uhttp://www.ams.org/mathscinet-getitem?mr=2039660
905    _aaw
906    _aaw
906    _aaw
995    _f02834-02
       _k28 AMB
       _eSalle R
995    _f02834-01
       _k28 AMB
       _eSalle R
001     10558
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