On V. Ramaswami's Tauberian Theorem of Oscillation Jump To References Section Authors S. Minakshisundaram Madras University ,IN DOI: https://doi.org/10.18311/jims/1939/17264 Abstract In this paper I give a simple and direct proof of Theorem A based on certain auxiliary theorems interesting in themselves. The method of proof closely resembles the one used by Szasz in some of his recent papers.