• [1] Garrett Birkhoff, Integration of functions with values in a Banach space, Trans. Amer. Math. Soc. 38 (1935), no. 2, 357–378. MR 1501815, http://dx.doi.org/10.1090/S0002-9947-1935-1501815-3
• [2] Nelson Dunford, Uniformity in linear spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 305–356. MR 1501971, http://dx.doi.org/10.1090/S0002-9947-1938-1501971-X
• [3] I. Gelfand, Sur un lemme de la théorie des espaces linéaires, Communications de l'Institut des Sciences Mathématiques et Mécaniques de l'Université de Kharkoff et la Société Mathématique de Kharkoff, vol. 13, pp. 35-40.
• [4] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277–304. MR 1501970, http://dx.doi.org/10.1090/S0002-9947-1938-1501970-8
• [5] A. Kolmogoroff, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Mathematica, vol. 5 (1934), pp. 29-33.
• [6] S. Banach, Théorie des Opérations Linéaires, Monografje Matematyczne, Warsaw, 1932.
• [7] John von Neumann, On complete topological spaces, Trans. Amer. Math. Soc. 37 (1935), no. 1, 1–20. MR 1501776, http://dx.doi.org/10.1090/S0002-9947-1935-1501776-7
• [8] John V. Wehausen, Transformations in linear topological spaces, Duke Math. J. 4 (1938), no. 1, 157–169. MR 1546041, http://dx.doi.org/10.1215/S0012-7094-38-00412-0
• [9] E. H. Moore, General Analysis, Memoirs of the American Philosophical Society, vol. 1, part 2, 1939.
• [10] E. H. Moore and H. L. Smith, A general theory of limits, American Journal of Mathematics, vol. 44 (1922), p. 103.
• [11] Fréchet, Sur l'intégrale d'une fonctionelle étendue à un ensemble abstrait, Bulletin de la Société Mathématique de France, vol. 43 (1915), pp. 248-265.
• [12] S. Saks, Addition to the note on some functionals, these Transactions, vol. 35 (1933), p. 967.
• [13] S. Bochner, Integration von Funktionen deren Werte die Elemente eines Vektorraumes sind, Fundamenta Mathematicae, vol. 20 (1933), pp. 262-276.
• [14] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, http://dx.doi.org/10.1090/S0002-9947-1936-1501880-4
• [15] B. J. Pettis, A note on regular Banach spaces, Bull. Amer. Math. Soc. 44 (1938), no. 6, 420–428. MR 1563761, http://dx.doi.org/10.1090/S0002-9904-1938-06775-4
• [16] Nelson Dunford and Anthony P. Morse, Remarks on the preceding paper of James A. Clarkson: “Uniformly convex spaces” [Trans. Amer. Math. Soc. 40 (1936), no. 3; 1 501 880], Trans. Amer. Math. Soc. 40 (1936), no. 3, 415–420. MR 1501881, http://dx.doi.org/10.1090/S0002-9947-1936-1501881-6
• [17] C. Carathéodory, Vorlesungen über reelle Funktionen, Leipzig, 1918.
• [18] Garrett Birkhoff, A note on topological groups, Compositio Math. 3 (1936), 427–430. MR 1556955
• [19] T. H. Hildebrandt, Linear operations on functions of bounded variation, Bull. Amer. Math. Soc. 44 (1938), no. 2, 75. MR 1563684, http://dx.doi.org/10.1090/S0002-9904-1938-06685-2
• [20] K. Knopp, Mengentheoretische Behandlung einiger Probleme der diophantischen Approximationen und der transfiniten Wahrscheinlichkeiten, Mathematische Annalen, vol. 95 (1925), pp. 409-420.
• [21] W. Sierpiński, Hypothèse du Continu, Monografje Matematyczne, Warsaw, 1934.
• [22] G. H. Hardy and J. E. Littlewood, Some problems of diophantine approximation, Acta Mathematica, vol. 37 (1914), pp. 155-190.
• [23] B. J. Pettis, Differentiation in Banach spaces, Duke Math. J. 5 (1939), no. 2, 254–269. MR 1546122, http://dx.doi.org/10.1215/S0012-7094-39-00523-5

Bibliography

[1]

G. Birkhoff, Integration of functions with values in a Banach space, these Transactions, vol. 38 (1935), pp. 357-378. MR 1501815

[2]

N. Dunford, Uniformity in linear spaces, these Transactions, vol. 44 (1938), pp. 305-356. MR 1501971

[3]

I. Gelfand, Sur un lemme de la théorie des espaces linéaires, Communications de l'Institut des Sciences Mathématiques et Mécaniques de l'Université de Kharkoff et la Société Mathématique de Kharkoff, vol. 13, pp. 35-40.

[4]

B. J. Pettis, On integration in vector spaces, these Transactions, vol. 44 (1938), pp. 277-304. MR 1501970

[5]

A. Kolmogoroff, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Mathematica, vol. 5 (1934), pp. 29-33.

[6]

S. Banach, Théorie des Opérations Linéaires, Monografje Matematyczne, Warsaw, 1932.

[7]

J. von Neumann, On complete topological spaces, these Transactions, vol. 37 (1935), pp. 1-20. MR 1501776

[8]

J. V. Wehausen, Transformations in linear topological spaces, Duke Mathematical Journal, vol. 4 (1938), pp. 157-169. MR 1546041

[9]

E. H. Moore, General Analysis, Memoirs of the American Philosophical Society, vol. 1, part 2, 1939.

[10]

E. H. Moore and H. L. Smith, A general theory of limits, American Journal of Mathematics, vol. 44 (1922), p. 103.

[11]

Fréchet, Sur l'intégrale d'une fonctionelle étendue à un ensemble abstrait, Bulletin de la Société Mathématique de France, vol. 43 (1915), pp. 248-265.

[12]

S. Saks, Addition to the note on some functionals, these Transactions, vol. 35 (1933), p. 967.

[13]

S. Bochner, Integration von Funktionen deren Werte die Elemente eines Vektorraumes sind, Fundamenta Mathematicae, vol. 20 (1933), pp. 262-276.

[14]

J. A. Clarkson, Uniformly convex spaces, these Transactions, vol. 40 (1936), pp. 396-414. MR 1501880

[15]

B. J. Pettis, A note on regular Banach spaces, Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 420-428. MR 1563761

[16]

N. Dunford and A. P. Morse, Remarks on the preceding paper of James A. Clarkson, these Transactions, vol. 40 (1936), pp. 415-420. MR 1501881

[17]

C. Carathéodory, Vorlesungen über reelle Funktionen, Leipzig, 1918.

[18]

G. Birkhoff, A note on topological groups, Compositio Mathematica, vol. 3 (1936), pp. 427-430. MR 1556955

[19]

T. H. Hildebrandt, Linear Operations on functions of bounded variation, Bulletin of the American Mathematical Society, vol. 44 (1938), p. 75. MR 1563684

[20]

K. Knopp, Mengentheoretische Behandlung einiger Probleme der diophantischen Approximationen und der transfiniten Wahrscheinlichkeiten, Mathematische Annalen, vol. 95 (1925), pp. 409-420.

[21]

W. Sierpiński, Hypothèse du Continu, Monografje Matematyczne, Warsaw, 1934.

[22]

G. H. Hardy and J. E. Littlewood, Some problems of diophantine approximation, Acta Mathematica, vol. 37 (1914), pp. 155-190.

[23]

B. J. Pettis, Differentiation in Banach spaces, Duke Mathematical Journal, vol. 5 (1939), pp. 254-269. MR 1546122