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On the semi-continuity of double integrals in parametric form
Author:
Tibor Radó
Journal:
Trans. Amer. Math. Soc. 51 (1942), 336-361
MSC:
Primary 27.2X
MathSciNet review:
0005905
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References |
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Additional Information
- [1]
S. Banach Sur une classe de fonctions d'ensemble, Fundamenta Mathematicae, vol. 6 (1924), pp. 170-188.
- [1]
Gilbert
Ames Bliss, The Weierstrass 𝐹-function for
problems of the calculus of variations in space, Trans. Amer. Math. Soc. 15 (1914), no. 4, 369–378. MR
1500985, http://dx.doi.org/10.1090/S0002-9947-1914-1500985-7
- [1]
Philip
Franklin and Norbert
Wiener, Analytic approximations to topological
transformations, Trans. Amer. Math. Soc.
28 (1926), no. 4,
762–785. MR
1501373, http://dx.doi.org/10.1090/S0002-9947-1926-1501373-8
- [1]
E.
J. McShane, On the semi-continuity of double integrals in the
calculus of variations, Ann. of Math. (2) 33 (1932),
no. 3, 460–484. MR
1503070, http://dx.doi.org/10.2307/1968529
- [2]
E.
J. McShane, Integrals over surfaces in parametric form, Ann.
of Math. (2) 34 (1933), no. 4, 815–838. MR
1503135, http://dx.doi.org/10.2307/1968701
- [1]
Charles
B. Morrey Jr., A Class of Representations of Manifolds. Part
I, Amer. J. Math. 55 (1933), no. 1-4,
683–707. MR
1507929, http://dx.doi.org/10.2307/2371162
- [1]
Tibor
Rado, A Remark on the Area of Surfaces, Amer. J. Math.
58 (1936), no. 3, 598–606. MR
1507184, http://dx.doi.org/10.2307/2370978
- [2]
-On the derivative of the Lebesgue area of continuous surfaces, Fundamenta Mathematicae, vol. 30 (1938), pp. 34-39.
- [3]
-On absolutely continuous transformations in the plane, Duke Mathematical Journal, vol. 4 (1938), pp. 190-221.
- [4]
Tibor
Radó, On a lemma of McShane, Ann. of Math. (2)
42 (1941), 73–83. MR 0003433
(2,219b)
- [1]
- S. Banach Sur une classe de fonctions d'ensemble, Fundamenta Mathematicae, vol. 6 (1924), pp. 170-188.
- [1]
- G. A. Bliss The Weierstrass
-function for problems of the calculus of variations in space, these Transactions, vol. 15 (1914), pp. 369-378. MR 1500985
- [1]
- P. Franklin and N. Wiener Analytical approximations to topological transformations, these Transactions, vol. 28 (1926), pp. 762-785. MR 1501373
- [1]
- E. J. McShane On the semi-continuity of double integrals in the calculus of variations, Annals of Mathematics, (2), vol. 33 (1932), pp. 460-184. MR 1503070
- [2]
- -Integrals over surfaces in parametric form, Annals of Mathematics, (2), vol. 34 (1933), pp. 815-838. MR 1503135
- [1]
- C. B. Morrey A class of representations of manifolds, I, American Journal of Mathematics, vol. 55 (1933), pp. 683-707. MR 1507929
- [1]
- T. Radó A remark on the area of surfaces, American Journal of Mathematics, vol. 58 (1936), pp. 598-606. MR 1507184
- [2]
- -On the derivative of the Lebesgue area of continuous surfaces, Fundamenta Mathematicae, vol. 30 (1938), pp. 34-39.
- [3]
- -On absolutely continuous transformations in the plane, Duke Mathematical Journal, vol. 4 (1938), pp. 190-221.
- [4]
- -On a lemma of McShane, Annals of Mathematics, (2), vol. 42 (1941), pp. 73-83. MR 0003433 (2:219b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1942-0005905-X
PII:
S 0002-9947(1942)0005905-X
Article copyright:
© Copyright 1942 American Mathematical Society
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