In probability theory, Yan's theorem is a separation and existence result. It is of particular interest in financial mathematics where one uses it to prove the Kreps-Yan theorem. The theorem was published by Jia-An Yan. It was proven for the L1 space and later generalized by Jean-Pascal Ansel to the case . Yan's theorem Notation: is the closure of a set . . is the indicator function of . is the conjugate index of . Statement Let be a probability space, and be the space of non-negative and bounded random variables. Further let be a convex subset and . Then the following three conditions are equivalent: For all with exists a constant , such that . For all with exists a constant , such that . There exists a random variable , such that almost surely and . Literature Freddy Delbaen and Walter Schachermayer: The Mathematics of Arbitrage (2005). Springer Finance References Probability