The notion of (O,∞) - valued submeasure is of interest since submeasures can be used to generate a ring topology, thereby creating a natural setting for the consideration of continuity in relation to topological group-valued set functions. Regarding submeasures an exhaustion principle which enables to establish a Lebesgue decomposition theorem for these submeasures. The methods are those which were used by Drewnowski and main theorems of this note generalize theorems 4.7 and 6.7