The transformation of double integrals
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- by R. G. Helsel and T. Radó PDF
- Trans. Amer. Math. Soc. 54 (1943), 83-102 Request permission
References
- H. E. Bray, Proof of a formula for an area, Bull. Amer. Math. Soc. 29 (1923), no. 6, 264–270. MR 1560720, DOI 10.1090/S0002-9904-1923-03721-X G. Fubini Sulla derivata seconda mista di un integrale doppio, Rend. Cir. Mat. Palermo vol. 40 (1915) pp. 297- 98
- R. G. Helsel and P. M. Young, Characterization theorems for integral means, Duke Math. J. 10 (1943), 259–269. MR 8425
- E. J. McShane, Integrals over surfaces in parametric form, Ann. of Math. (2) 34 (1933), no. 4, 815–838. MR 1503135, DOI 10.2307/1968701
- Charles B. Morrey Jr., A Class of Representations of Manifolds. Part I, Amer. J. Math. 55 (1933), no. 1-4, 683–707. MR 1507929, DOI 10.2307/2371162
- Hans Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. 79 (1919), no. 4, 340–359 (German). MR 1511935, DOI 10.1007/BF01498415 T. Radó On continuous transformations in the plane, Fund. Math. vol. 27 (1936) pp. 201-211.
- Tibor Rado, A Remark on the Area of Surfaces, Amer. J. Math. 58 (1936), no. 3, 598–606. MR 1507184, DOI 10.2307/2370978
- Tibor Radó, On absolutely continuous transformations in the plane, Duke Math. J. 4 (1938), no. 1, 189–221. MR 1546044, DOI 10.1215/S0012-7094-38-00415-6
- T. Radó and P. Reichelderfer, A theory of absolutely continuous transformations in the plane, Trans. Amer. Math. Soc. 49 (1941), 258–307. MR 3698, DOI 10.1090/S0002-9947-1941-0003698-2 J. Schauder Über stetige Abbildungen, Fund. Math. vol. 12 (1928) pp. 47-74.
- C. De La Vallée Poussin, Sur l’intégrale de Lebesgue, Trans. Amer. Math. Soc. 16 (1915), no. 4, 435–501 (French). MR 1501024, DOI 10.1090/S0002-9947-1915-1501024-5 W. H. Young On a formula for an area, Proc. London Math. Soc. vol. 18 (1920) pp. 339-374. —On a new set of conditions for a formula for an area, Proc. London Math. Soc. vol. 21 (1923) pp. 75-94. —Integration over the area of a curve and transformation of the variables in a multiple integral, Proc. London Math. Soc. vol. 21 (1923) pp. 161-190.
Additional Information
- © Copyright 1943 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 54 (1943), 83-102
- MSC: Primary 27.2X
- DOI: https://doi.org/10.1090/S0002-9947-1943-0008253-8
- MathSciNet review: 0008253