Geometric Measure Theory

By H. Fédérer. 1969

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Citations in the corpus

k-NN Regression Adapts to Local Intrinsic Dimension (2011, background): “on We start with the following deﬁnition of doubling measure wh ich will lead to the notion of local dimension used in this work. We stay informal in developing the motivation and refer the reader to [11, 12, 13] for thorough overviews of the topic of metric space dimension and doubling measures. De”
Connecting topological Hopf singularities (2003, methodology): “for the groups of i dimensional integer-multiplicity rectifiable and locally rectifiable currents in R4 × S3 ([F], [S], [GMS2]).”
Sard's theorem for mappings in Hölder and Sobolev spaces (2005, unknown): “See Federer’s monograph [10], Theorem 2.”
Monte Carlo Confidence Sets for Identified Sets (2016, background): “near subspace of Rdim(g) of dimension dim() such that ’(N\fg() : 2 g) = \im(’) where im(’) is the image of ’. Such manifolds are also called dim()-dimensional submanifolds of class 2 of Rdim(g); seeFederer (1996), Chapers 3.1.19-20. 43 and4.4hold with equal to the tangent space of fg() : 2 gat the o”
Faber–Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach (2015, unknown): “The main references are [2,18,19].”
On the Space of BV Functions and a Related Stochastic Calculus in Infinite Dimensions (2001, background): “1) Thus the space BV(U ) is a natural extension of the classical Sobolev space W 1 (U ) with V(\)=&{\&1 and it has played important roles in solving diverse fine variational problems in finite dimensions ([9, 15, 8, 3]).”
Structure of level sets and Sard-type properties of Lipschitz maps (2013, background): “For more general formulations see [6], [9], Theorem 3.”
Real homotopy theory of semi-algebraic sets (2008, background): “A basic reference is Federer [6].”