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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The $\phi$ rectifiable subsets of the plane
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by A. P. Morse and John F. Randolph PDF
Trans. Amer. Math. Soc. 55 (1944), 236-305 Request permission
References
  • A. S. Besicovitch, On the fundamental geometrical properties of linearly measurable plane sets of points (II), Math. Ann. 115 (1938), no. 1, 296–329. MR 1513189, DOI 10.1007/BF01448943
    • C. CarathĂ©odory, Über das lineare Mass von Punktmengen—eine Verallgemeinerung des LĂ€ngenbegriffs, Nachr. Ges. Wiss. Göttingen, 1914, pp. 404-426. H. Hahn, Theorie der reellen Funktionen, vol. 1, Berlin, 1921. C. Kuratowski, Topologie I, Warsaw, 1933.
  • Anthony P. Morse, A theory of covering and differentiation, Trans. Amer. Math. Soc. 55 (1944), 205–235. MR 9974, DOI 10.1090/S0002-9947-1944-0009974-4
    • F. Roger, Sur quelque applications metriques de la notion de contingent bilateral, C. R. Acad. Sci. Paris vol. 201 (1935) pp. 28-30. S. Saks, Theory of the integral, Warsaw, 1937. T. Estermann, Über CarathĂ©odory und Minkowski Verallgemeinerungen des LĂ€ngenbegriffs, Abh. Math. Sem. Hamburgischen Univ., 1925, pp. 73-116. J. Favard, Une definition de la longeur et de l’aire, C. R. Acad. Sci. Paris vol. 194 (1932) pp. 344-346. W. Gross, Über des FlĂ€chenmass von Punktmengen, Monatshefte fĂŒr Mathematik und Physik vol. 27 (1918) pp. 145-176. —, Über des lineare Mass von Punktmengen, Monatshefte fĂŒr Mathematik und Physik vol. 28 (1918) pp. 177-193. O. Jansen, Über einige stetige Kurven, ĂŒber BogenlĂ€ngen, linearen Inhalt und FlĂ€cheninholt, Inaugural-Dissertation, Königsberg, 1907.
  • R. L. Jeffery, Sets of $k$-extent in $n$-dimensional space, Trans. Amer. Math. Soc. 35 (1933), no. 3, 629–647. MR 1501706, DOI 10.1090/S0002-9947-1933-1501706-6
    • H. Minkowski, Über die Begriffe LĂ€nge, OberflĂ€sche und Volumen, Jber. Deutschen Math. Verein. vol. 9 (1900) pp. 115-121.
  • Anthony P. Morse and John F. Randolph, Gillespie measure, Duke Math. J. 6 (1940), 408–419. MR 1832
    • J. P. Schauder, The theory of surface measure, Fund. Math. vol. 8 (1926) pp. 1-48. H. Steinhaus, Zur Praxis der Rektifikation und zum Langenbegriff, SĂ€chsische Akademie zu Leipzig, Berichte vol. 82 (1930) pp. 120-130. —, Sur la portĂ©e puratique et thĂ©orique de quelques thĂ©orĂšmes sur la mesure des ensembles de droites, Comptes rendus du premier congress des pays Slaves, 1929, pp. 348-354. W. H. Young and Grace Chisholm, The theory of sets of points, 1906.
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Additional Information
  • © Copyright 1944 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 55 (1944), 236-305
  • MSC: Primary 27.2X
  • DOI: https://doi.org/10.1090/S0002-9947-1944-0009975-6
  • MathSciNet review: 0009975