The following paper is available:
Cantor, G., Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, Mathematische Annalen, vol. 5, pp. 123-132 (1872).
The title of this paper may be translated into English as `On the generalization of a theorem from the theory of trigonometric series'. In this paper, Cantor introduces his well-known construction of the real number system in which each real number is represented as a Cauchy sequence of rational numbers. Two Cauchy sequences of rational numbers represent the same real number if and only if the difference of the two sequences converges to zero. Cantor uses this construction of the real number system in order to generalize a theorem he had earlier proved concerning the uniqueness of trigonometric series representations of functions on an interval.
The paper is available, in German, in the following formats: