Who was the first to prove the Monotone Class Lemma?

Question

Who was the first one to prove the Monotone Class Lemma in history? I learned that it is sort of equivalent to the $\pi$-$\lambda$ theorem in probability theory. Which theorem appeared first in history? I saw some textbook calls "Halmos's monotone class lemma". But I am not able to find the source of his paper.

Answer 1

Expanding on Daniel Fischer's answer, with the help of Google Translate (and some minor editing): According to Elstrodt,

There are a number of variants of Theorems 6.2 [the Monotone Class Theorem] and 6.7 in the literature. The oldest general version known to the author was given in 1927 by Wacław SIERPINSKI (Oeuvres choisis, Tome II. Warszawa: PWN-Editions Scientifiques de Pologne 1975, pp. 640-642), who gives a very clear proof using the principle of good sets. In this way he avoids the transfinite induction most often used in older works. SIERPINSKI even proves a necessary and sufficient criterion that corresponds to our Problem 6.2. His result was included in the textbook literature by Hans HAHN, Reelle Funktionen. Erster Teil: Punktfunktionen. Leipzig: Akademische Verlagsges. 1932, pp. 262, 33.2.61. A slightly different version of the statement can be found in Stanisław SAKS Theory of the integral. Second ed. Warszawa 1937. Nachdrucke: New York: Hafner Publ. Comp.; New York: Dover Publications 1964, p. 85, (9.7).

NOTE: Of these references, Saks is the only one cited by Halmos in his Measure Theory textbook.