Page and Wooders (1996) prove that the no-unbounded-arbitrage (NUBA)
condition introduced by Page (1987) is equivalent to the existence of a no
arbitrage price (NAPS) when no agent has non-null useless vectors. Al-
louch, Le Van and Page (2002) show that their generalized NAPS condition
is actually equivalent to the weak-no-market-arbitrage (WNMA) condition
introduced by Hart (1974). They mention that this result implies the one
given by Page andWooders (1996). In this note, we show that these results
are actually circular.