Paper, 'Über Reihen auf der Convergenzgrenze' [On series at the limit of convergence] by Emanuel Lasker The paper is divided into three chapters. A limit operation of any kind, for instance, simple or multiple integration; the formation of infinite sums or products; or any combination of these operations gives rise to certain typical considerations which form the subject of the first chapter. Annotations in pencil and ink throughout. Note on front reads 'Original paper - not printed - replaced by revised version March 1901.' Subject: Mathematics Received 15 March 1900. Read 5 April 1900. Communicated by [Percy Alexander] MacMahon. A version of this paper was published in volume 196 of the Philosophical Transactions of the Royal Society A as 'Über reihen auf der convergenzgrenze'. 1900