Published in short in 1947, in detail in 1949 in Russian and in 1952 (Rokhlin 1952) in English. An unpublished text of 1940 is mentioned in (Rokhlin 1952, page 2). "The theory of Lebesgue spaces in its present form was constructed by V. A. Rokhlin" (Sinai 1994, page 16). Rokhlin, V. A. (1952), On the fundamental ideas of measure theory(PDF), Translations, vol. 71, American Mathematical Society, pp. 1–54. Translated from Russian: Рохлин, В. А. (1949), "Об основных понятиях теории меры", Математический Сборник (Новая Серия), 25 (67): 107–150. Rokhlin, V. A. (1952), On the fundamental ideas of measure theory(PDF), Translations, vol. 71, American Mathematical Society, pp. 1–54. Translated from Russian: Рохлин, В. А. (1949), "Об основных понятиях теории меры", Математический Сборник (Новая Серия), 25 (67): 107–150. Sinai, Ya. G. (1994), Topics in ergodic theory, Princeton Univ. Press.