On the Number of Positive Sums of Independent Random Variables

2 . The invariance principle . We first prove the following : If the theorem can be established for one particular sequence of independent random variables Y1, Y2, . . . satisfying the conditions of the theorem then the conclusion of the theorem holds for all sequences of independent random variables which satisfy the conditions of the theorem . In other words, if the limiting distribution exists it is independent of the distributions of the individual X's . Let