In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ what seems to be 2 inconsistent definitions of arbitrage:
The first definition is for the single period Binomial model
The second definition is for the multi period Binomial model
The second suggests that there is a possibility of the portfolio value ending up zero while the first does not...
...Why?
Edit: Oh, I forgot to mention: My prof uses the latter definition to replace the first definition for the one-period. E said something about different conditions or something. (I'll ask about it during next consultation hours.)