= Solution
For a finite-state, finite-horizon discrete-time frictionless market with a strictly positive <numéraire>, the <fundamental theorem of asset pricing> states \b[no arbitrage if and only if there exists an <equivalent martingale measure>] under which all discounted asset prices are <martingales>. Equivalence means the same null events as the physical measure. In this setting <market completeness> is equivalent to uniqueness of the <equivalent martingale measure>, and a replicable payoff $H$ has price $S_t^0\mathbb E_Q[H/S_T^0\mid\mathcal F_t]$. Without finite-state hypotheses, stronger integrability and closure conditions are needed; this is the standard multi-period course version.
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