He focused particularly on surface area, rectifiability of sets, and the extent to which one could substitute rectifiability for smoothness in the analysis of surfaces.
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He focused particularly on surface area, rectifiability of sets, and the extent to which one could substitute rectifiability for smoothness in the analysis of surfaces.
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His book " Geometry of Sets and Measures in Euclidean Spaces : Fractals and Rectifiability " is now a widely cited and a standard textbook in this field.
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Federer is perhaps best known for his treatise " Geometric Measure Theory ", published in 1969 . Intended as both a text and a reference work, the book is unusually complete, general and authoritative : its nearly 600 pages cover a substantial amount of linear and multilinear algebra, give a profound treatment of measure theory, integration and differentiation, and then move on to rectifiability, theory of currents, and finally, variational applications.
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