A common formulation of the martingale convergence theorem for discrete-time martingales is the following. Hunter bits, bridles, crops, spurs, and martingales are tightly regulated. Stout (1970) generalized the LIL to stationary ergodic martingales. Running martingales are also allowed, but must be used with rein stops. Standing and Irish martingales are not allowed. In this aspect, discrete-time martingales generalize the idea of partial sums of independent random variables. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. For this reason, standing martingales are not used in show jumping or eventing. The following argument is due to Kareem Amin and employs discrete martingales. Almost all shows prohibit martingales in "flat" or "under saddle" (not to jump) classes. Standing martingales are allowed for all over fence classes. Schnorr gave a third equivalent definition in terms of martingales. Martingales can also be built from other martingales. Trees in a Banach space are a special instance of vector-valued martingales. Martingales with continuous time parameter can also be considered.