We provide a new axiomatization of the core of games in characteristic form. The games may have either finite sets of players or continuum sets of players and finite coalitions. Our research is based on Peleg's axiomatization for finite games and on the notions of measurement-consistent partitions and the f-core introduced by Kaneko and Wooders. Since coalitions are finite in both finite games and in continuum games, we can use the reduced game property and the converse reduced game property for our axiomatization. Both properties are particularly appealing in large economies.