References
Alfsen, E. M.: Order theoretic foundations of integration. Math. Ann.149, 419–461 (1963).
Banach, S.: Sur le théorème de M. Vitali. Fundamenta Math.5, 130–136 (1924).
Carathéodory, C.: Vorlesungen über reelle Funktionen. Berlin, Leipzig 1918.
Comfort, W. W., andHugh Gordon: Vitali's theorem for invariant measures. Trans. Am. Math. Soc.99, 83–90 (1961).
Doob, J. L.: Stochastic processes. New York, London 1953.
Hahn, H., andA. Rosenthal: Set functions. Albuquerque 1948.
Haupt, O., G. Aumann u.C. Y. Pauc: Differential und Integralrechnung. Berlin 1955.
——, u.C. Y. Pauc: Halobedingungen und Vitalische Eigenschaft von Somensystemen. Arch. Math.4, 107–114 (1953).
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).
Krickeberg, K.: Extreme Derivierte von Zellenfunktionen in Booleschen σ-Algebren und ihre Integration. Sitz.-Ber. Bayer. Akad. der Wissenschaften 217–279 (1955).
Krickeberg, K.: Convergence of martingales with a directed index set. Trans. Am. Math. Soc.83, 313–337 (1956).
-- Seminar on martingales. Mat. Inst. Aarhus Univ. 1959.
-- Notwendige Konvergenzbedingungen bei Martingalen und verwandten Prozessen. Trans. 2nd Prague Conf. on Information theory etc., Prague 1959.
—— Absteigende Semimartingale mit filtrierendem Parameterbereich. Abhandl. math. Seminar hamburg. Univ.24, 109–125 (1960).
——, etC. Pauc: Martingales et dérivation. Bull. soc. math. France91, 455–544 (1963).
de la Vallée Poussin, C.: Intégrales de Lebesgue, fonctions d'ensemble, classes de Baire. 2e édition. Paris 1934.
Morse, A. P.: A theory of covering and differentiation. Trans. Am. Math. Soc.55, 205–235 (1944).
Munroe, M. E.: Introduction to measure and integration. Cambridge Mass. 1953.
Pauc, C.: Ableitungsbasen, Prätopologie und starker Vitalischer Satz. J. reine angew. Math.191, 69–91 (1953).
Saks, S.: Theory of the integral. 2nd edition. Warszawa 1937.
Vitali, G.: Sui gruppi di punti e sulle funzioni di variabili reali. Atti Accad. Sci. Torino43, 75–92 (1908).
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Alfsen, E.M. Some covering theorems of Vitali type. Math. Ann. 159, 203–216 (1965). https://doi.org/10.1007/BF01360291
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DOI: https://doi.org/10.1007/BF01360291