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A geometric theory of surface area. I: Non-parametric surfaces. (English) Zbl 0224.50002

MSC:
51M25 Length, area and volume in real or complex geometry
28A75 Length, area, volume, other geometric measure theory
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References:
[1] Serret, J. A.: Cours de calcul différentiel et intégral. Paris, 1868.
[2] Lebesgue, H.: Intégrale, longeur, aire. Ann. Mat. Pura ed Appl. (3)7, 231-359 (1902). · JFM 33.0307.02
[3] Geöcze, Z. de: Quadrature de surfaces courbes. Math. Naturwiss. Berichte Ung.26 (1910). · JFM 44.0706.01
[4] Mulholland, H. P.: On Geöcze’s problem for non-parametric surfaces. Trans. Amer. Math. Soc.68, 330-336 (1950). · Zbl 0037.04102
[5] Young, W. H.: On the triangulation method of defining the area of a surface. Proc. London Math. Soc. 2nd Series19, 117-152 (1919). · JFM 47.0242.01
[6] Rademacher, M.: Über partielle und totale Differenzierbarkeit II. Math. Ann.81, 52-63 (1920). · JFM 47.0243.01
[7] Kempisty, S.: Sur la méthode triangulaire du calcul de l’aire d’une surface courbe. Bull. Soc. Math. de France64, 119-132 (1936). · Zbl 0015.01003
[8] Besicovitch, A. S.: On the definition of the area of a surface by means of inscribed polyhedra. Journal London Math. Soc.19, 138-141 (1944). · Zbl 0061.10603
[9] Toralballa, L. V.: Directional deviation norms and surface area. L’Enseignement Math., IIe Serie13, 111-118 (1967). · Zbl 0155.10402
[10] Toralballa, L. V.: Piecewise flatness and surface area. Annales Polonici Mathematici21, 223-230 (1969). · Zbl 0174.53803
[11] Radó, T.: Length and area. Amer. Math. Soc., Colloquium Publications (1948).
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