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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Topics on Analysis in Metric Spaces (Hardcover)
Loot Price: R3,358
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Topics on Analysis in Metric Spaces (Hardcover)
Series: Oxford Lecture Series in Mathematics and Its Applications, 25
Expected to ship within 10 - 15 working days
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This book presents the main mathematical prerequisites for analysis
in metric spaces. It covers abstract measure theory, Hausdorff
measures, Lipschitz functions, covering theorums, lower
semicontinuity of the one-dimensional Hausdorff measure, Sobolev
spaces of maps between metric spaces, and Gromov-Hausdorff theory,
all developed ina general metric setting. The existence of
geodesics (and more generally of minimal Steiner connections) is
discussed on general metric spaces and as an application of the
Gromov-Hausdorff theory, even in some cases when the ambient space
is not locally compact. A brief and very general description of the
theory of integration with respect to non-decreasing set functions
is presented following the Di Giorgi method of using the
'cavalieri' formula as the definition of the integral. Based on
lecture notes from Scuola Normale, this book presents the main
mathematical prerequisites for analysis in metric spaces.
Supplemented with exercises of varying difficulty it is ideal for a
graduate-level short course for applied mathematicians and
engineers.
General
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