  We study the Fundamental Theorem of Asset Pricing for a general financial
market under Knightian Uncertainty. We adopt a functional analytic approach
which require neither specific assumptions on the class of priors $\mathcal{P}$
nor on the structure of the state space. Several aspects of modeling under
Knightian Uncertainty are considered and analyzed. We show the need for a
suitable adaptation of the notion of No Free Lunch with Vanishing Risk and
discuss its relation to the choice of an appropriate filtration. In an abstract
setup, we show that absence of arbitrage is equivalent to the existence of
\emph{approximate} martingale measures sharing the same polar set of
$\mathcal{P}$. We then specialize the results to a discrete-time framework in
order to obtain true martingale measures.
