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Currents and area
Author:
Hebert Federer
Journal:
Trans. Amer. Math. Soc. 98 (1961), 204-233
MSC:
Primary 28.80
MathSciNet review:
0123682
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
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Lamberto
Cesari, Surface area, Annals of Mathematics Studies, no. 35,
Princeton University Press, Princeton, N. J., 1956. MR 0074500
(17,596b)
- [M]
Maurice
R. Demers and Herbert
Federer, On Lebesgue area. II, Trans. Amer. Math. Soc. 90 (1959), 499–522. MR 0102586
(21 #1376), http://dx.doi.org/10.1090/S0002-9947-1959-0102586-4
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deRham DR. Variétés différentiables, Actualités Sci. Ind. no. 1222, Paris, Hermann et Cie, 1955.
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Eilenberg E. On
measures, Ann. Soc. Polon. Math. vol. 17 (1938) pp. 252-253.
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Herbert
Federer, Surface area. I, Trans. Amer. Math. Soc. 55 (1944), 420–437. MR 0010610
(6,44d), http://dx.doi.org/10.1090/S0002-9947-1944-0010610-1
- 1.
Herbert
Federer, Coincidence functions and their
integrals, Trans. Amer. Math. Soc. 59 (1946), 441–466. MR 0015466
(7,422a), http://dx.doi.org/10.1090/S0002-9947-1946-0015466-0
- 2.
Herbert
Federer, The (𝜙,𝑘) rectifiable
subsets of 𝑛-space, Trans. Amer.
Soc. 62 (1947),
114–192. MR 0022594
(9,231c), http://dx.doi.org/10.1090/S0002-9947-1947-0022594-3
- 3.
Herbert
Federer, Essential multiplicity and Lebesgue area, Proc. Nat.
Acad. Sci. U. S. A. 34 (1948), 611–616. MR 0027837
(10,361e)
- 4.
Herbert
Federer, Hausdorff measure and Lebesgue area, Proc. Nat. Acad.
Sci. U. S. A. 37 (1951), 90–94. MR 0047128
(13,831f)
- 5.
Herbert
Federer, Measure and area, Bull. Amer. Math. Soc. 58 (1952), 306–378. MR 0049289
(14,149e), http://dx.doi.org/10.1090/S0002-9904-1952-09586-0
- 6.
Herbert
Federer, Some integralgeometric
theorems, Trans. Amer. Math. Soc. 77 (1954), 238–261. MR 0063686
(16,163b), http://dx.doi.org/10.1090/S0002-9947-1954-0063686-6
- 7.
Herbert
Federer, On Lebesgue area, Ann. of Math. (2)
61 (1955), 289–353. MR 0067178
(16,683a)
- 8.
Herbert
Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418–491. MR 0110078
(22 #961), http://dx.doi.org/10.1090/S0002-9947-1959-0110078-1
- 9.
Hebert
Federer, The area of a nonparametric
surface, Proc. Amer. Math. Soc. 11 (1960), 436–439. MR 0123681
(23 #A1005), http://dx.doi.org/10.1090/S0002-9939-1960-0123681-3
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Herbert
Federer and Wendell
H. Fleming, Normal and integral currents, Ann. of Math. (2)
72 (1960), 458–520. MR 0123260
(23 #A588)
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Witold
Hurewicz and Henry
Wallman, Dimension Theory, Princeton Mathematical Series, v.
4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
(3,312b)
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Charles
B. Morrey Jr., An Analytic Characterization of Surfaces of Finite
Lebesgue Area. Part I, Amer. J. Math. 57 (1935),
no. 3, 692–702. MR
1507104, http://dx.doi.org/10.2307/2371197
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Radó R. Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948.
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Paul
Slepian, Theory of Lebesgue area of continuous maps of 2-manifolds
into 𝑛-space, Ann. of Math. (2) 68 (1958),
669–689. MR 0098819
(20 #5271)
- 10.
Paul
Slepian, On the Lebesgue area of a doubled map, Pacific J.
Math. 8 (1958), 613–620. MR 0132156
(24 #A2003)
- [H]
Hassler
Whitney, Geometric integration theory, Princeton University
Press, Princeton, N. J., 1957. MR 0087148
(19,309c)
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Laurent
Chisholm Young, Surfaces paramétriques
généralisées, Bull. Soc. Math. France
79 (1951), 59–84 (French). MR 0046421
(13,731c)
- [L]
- Cesari C. Surface area, Annals of Mathematics Studies no. 35, Princeton, N. J., Princeton University Press, 1956. MR 0074500 (17:596b)
- [M]
- R. Demers and H. Federer DF. On Lebesgue area. II, Trans. Amer. Math. Soc. vol. 90 (1959) pp. 499-522. MR 0102586 (21:1376)
- [G]
- deRham DR. Variétés différentiables, Actualités Sci. Ind. no. 1222, Paris, Hermann et Cie, 1955.
- [S]
- Eilenberg E. On
measures, Ann. Soc. Polon. Math. vol. 17 (1938) pp. 252-253.
- [H]
- Federer F1. Surface area. I, Trans. Amer. Math. Soc. vol. 55 (1944) pp. 420-437. MR 0010610 (6:44d)
- 1.
- -F2. Coincidence functions and their integrals, Trans. Amer. Math. Soc. vol. 59 (1946) pp. 441-466. MR 0015466 (7:422a)
- 2.
- -F3. The
rectifiable subsets of n space, Trans. Amer. Math. Soc. vol. 62 (1947) pp. 114-192. MR 0022594 (9:231c)
- 3.
- -F4. Essential multiplicity and Lebesgue area, Proc. Nat. Acad. Sci. U.S.A. vol. 34 (1948) pp. 611-616. MR 0027837 (10:361e)
- 4.
- -F5. Hausdorff measure and Lebesgue area, Proc. Nat. Acad. Sci. U.S.A. vol. 37 (1951) pp. 90-94. MR 0047128 (13:831f)
- 5.
- -F6. Measure and area, Bull. Amer. Math. Soc. vol. 58 (1952) pp. 306-378. MR 0049289 (14:149e)
- 6.
- -F7. Some integralgeometric theorems, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 238-261. MR 0063686 (16:163b)
- 7.
- -F8. On Lebesgue area, Ann. of Math. vol. 61 (1955) pp. 289-353. MR 0067178 (16:683a)
- 8.
- -F9. Curvature measures, Trans. Amer. Math. Soc. vol. 93 (1959) pp. 418-491. MR 0110078 (22:961)
- 9.
- -F10. The area of a nonparametric surface, Proc. Amer. Math. Soc. vol. 63 (1960) pp. 436-439. MR 0123681 (23:A1005)
- [H]
- Federer and W. H. Fleming FF. Normal and integral currents, Ann. of Math. vol. 72 (1960) pp. 458-520. MR 0123260 (23:A588)
- [W]
- Hurewicz and H. Wallman HW. Dimension theory, Princeton, N. J., Princeton University Press, 1941. MR 0006493 (3:312b)
- [C]
- B. Morrey, Jr. M. An analytic characterization of surfaces of finite Lebesgue area, Amer. J. Math. vol. 57 (1935) pp. 692-702. MR 1507104
- [T]
- Radó R. Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948.
- [P]
- Slepian S1. Theory of Lebesgue area for continuous maps of 2-manifolds into n-space, Ann. of Math. vol. 68 (1958) pp. 669-689. MR 0098819 (20:5271)
- 10.
- -S2. On the Lebesgue area of a doubled map, Pacific J. Math. vol. 8 (1958) pp. 613-620. MR 0132156 (24:A2003)
- [H]
- Whitney W. Geometric integration theory, Princeton, N. J., Princeton University Press, 1957. MR 0087148 (19:309c)
- [L]
- C. Young Y. Surfaces paramétriques généralisées, Bull. Soc. Math. France vol. 79 (1951) pp. 59-84. MR 0046421 (13:731c)
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DOI:
http://dx.doi.org/10.1090/S0002-9947-1961-0123682-0
PII:
S 0002-9947(1961)0123682-0
Article copyright:
© Copyright 1961 American Mathematical Society
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