Sentence:  Is it possible to find events "A", "B" of "&Omega;" so that "A" and "B" are independent? The answer to this simple and interesting problem is no. A probability space ("&Omega;","&Sigma;","P") is called a “<WSD>"dependent</WSD> probability space"” if there are no nontrivial independent events in "&Omega;", ("&Omega;","&Sigma;","P") is called an "independent space" otherwise. 
Meaning of the word marked with <WSD> tags:  Having a probability that is affected by the outcome of a separate event.