×

Some covering theorems of Vitali type. (English) Zbl 0145.05401

References:

[1] Alfsen, E. M.: Order theoretic foundations of integration. Math. Ann.149, 419-461 (1963). · Zbl 0111.25605 · doi:10.1007/BF01397977
[2] Banach, S.: Sur le théorème de M. Vitali. Fundamenta Math.5, 130-136 (1924). · JFM 50.0143.02
[3] Carathéodory, C.: Vorlesungen über reelle Funktionen. Berlin, Leipzig 1918. · JFM 46.0376.12
[4] Comfort, W. W., andHugh Gordon: Vitali’s theorem for invariant measures. Trans. Am. Math. Soc.99, 83-90 (1961). · Zbl 0104.04702
[5] Doob, J. L.: Stochastic processes. New York, London 1953. · Zbl 0053.26802
[6] Hahn, H., andA. Rosenthal: Set functions. Albuquerque 1948. · Zbl 0033.05301
[7] Haupt, O., G. Aumann u.C. Y. Pauc: Differential und Integralrechnung. Berlin 1955.
[8] ??, u.C. Y. Pauc: Halobedingungen und Vitalische Eigenschaft von Somensystemen. Arch. Math.4, 107-114 (1953). · Zbl 0050.27802 · doi:10.1007/BF01899670
[9] Hayes, C. A., andC. Y. Pauc: Full individual and class differentiation theorems and their relations to halo and Vitali properties. Canad. J. Math.7, 221-274 (1955). · Zbl 0068.04602 · doi:10.4153/CJM-1955-028-9
[10] Krickeberg, K.: Extreme Derivierte von Zellenfunktionen in Booleschen ?-Algebren und ihre Integration. Sitz.-Ber. Bayer. Akad. der Wissenschaften 217-279 (1955). · Zbl 0072.04501
[11] Krickeberg, K.: Convergence of martingales with a directed index set. Trans. Am. Math. Soc.83, 313-337 (1956). · Zbl 0083.27501 · doi:10.1090/S0002-9947-1956-0091328-4
[12] – Seminar on martingales. Mat. Inst. Aarhus Univ. 1959.
[13] – Notwendige Konvergenzbedingungen bei Martingalen und verwandten Prozessen. Trans. 2nd Prague Conf. on Information theory etc., Prague 1959.
[14] ?? Absteigende Semimartingale mit filtrierendem Parameterbereich. Abhandl. math. Seminar hamburg. Univ.24, 109-125 (1960). · Zbl 0099.12501 · doi:10.1007/BF02942024
[15] ??, etC. Pauc: Martingales et dérivation. Bull. soc. math. France91, 455-544 (1963).
[16] de la Vallée Poussin, C.: Intégrales de Lebesgue, fonctions d’ensemble, classes de Baire. 2e édition. Paris 1934. · JFM 60.0193.06
[17] Morse, A. P.: A theory of covering and differentiation. Trans. Am. Math. Soc.55, 205-235 (1944). · Zbl 0063.04111
[18] Munroe, M. E.: Introduction to measure and integration. Cambridge Mass. 1953. · Zbl 0050.05603
[19] Pauc, C.: Ableitungsbasen, Prätopologie und starker Vitalischer Satz. J. reine angew. Math.191, 69-91 (1953). · Zbl 0050.27901 · doi:10.1515/crll.1953.191.69
[20] Saks, S.: Theory of the integral. 2nd edition. Warszawa 1937. · Zbl 0017.30004
[21] Vitali, G.: Sui gruppi di punti e sulle funzioni di variabili reali. Atti Accad. Sci. Torino43, 75-92 (1908). · JFM 39.0101.05
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.