Crossing points of distributions and a theorem that relates them to second order stochastic dominance

We state formal definitions for crossing points in pairs of distributions and give a detailed proof of a theorem that relates those points to the second order stochastic dominance (SSD). The theorem states that the fulfillment of the area balance conditions for SSD at the tt values that correspond to crossing points, and at the limit t→∞t→∞, is a necessary and sufficient condition for its fulfillment at all tt: {−∞