The goal of this book is to associate to a large class of subsets of EN a signed measure which allows us to evaluate their geometry. In many cases (convex subsets and smooth subsets), one tool is the computation of the volume of tubular neighborhoods. That is why measure theory is indispensable in our context. We summarize in this chapter the main constructions and results on outer measures, measures, and signed measures ([43, 53, 63] are the basic references).
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Elements of Measure Theory. In: Generalized Curvatures. Geometry and Computing, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73792-6_5
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DOI: https://doi.org/10.1007/978-3-540-73792-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73791-9
Online ISBN: 978-3-540-73792-6
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