= Equivalent local martingale measures exclude admissible arbitrage
Suppose a finite-horizon market has a strictly positive <numéraire> $B$ and an equivalent measure under which all prices $S^i/B$ are <local martingales>. The discounted wealth of a <self-financing strategy> is a <stochastic integral> against those prices. If it is bounded below by a deterministic constant, that wealth is a <supermartingale>: add the lower-bound constant to obtain a <nonnegative local martingale>, then apply conditional Fatou to a localizing sequence. A zero-cost admissible <portfolio> therefore has expected discounted terminal wealth at most zero. Nonnegative terminal wealth with positive probability of a strict gain would have strictly positive expectation under the equivalent measure, a contradiction. Thus there is no admissible <arbitrage>. True <martingales> are not needed for this implication.
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