  We give characterizations of asymptotic arbitrage of the first and second
kind and of strong asymptotic arbitrage for large financial markets with small
proportional transaction costs $\la_n$ on market $n$ in terms of contiguity
properties of sequences of equivalent probability measures induced by
$\la_n$--consistent price systems. These results are analogous to the
frictionless case. Our setting is simple, each market $n$ contains two assets
with continuous price processes. The proofs use quantitative versions of the
Halmos--Savage Theorem and a monotone convergence result of nonnegative local
martingales. Moreover, we present an example admitting a strong asymptotic
arbitrage without transaction costs; but with transaction costs $\la_n>0$ on
market $n$ ($\la_n\to0$ not too fast) there does not exist any form of
asymptotic arbitrage.
