Sammendrag
In this paper we use some ideas of Cornet and de Boisdeffre to study the concept of arbitrage under asymmetric information. The mathematical framework is a separable probability space where the agents' information are represented by $\sigma$-algebras. In this setting we formulate some versions of the fundamental theorem of asset pricing (aka the Dalang-Morton-Willinger theorem) for the case of asymmetric information. We also study the revealing properties of no-arbitrage prices and prove that the results of Cornet and de Boisdeffre hold in a more general setting.