`  :``Probability, Random Variables and Stochastic Processes`` by Papoulis and Pillai states, ``if an event N equals the impossible event with probability 1 then P(N) = 0. This does not, of course, mean that N [is equal to the impossible event]``. This agrees with Coffee2theorems' comment ``...P(E) = 0 does not imply in general that E is impossible.`` I am however not familiar with other textbooks and so will not edit the article.   `