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It seems you can just state or describe some elements, here countable subsets as being in the sample space yet with measure zero and others as not being in the sample space and avoid any confusion.sysprog said:Only the impossible actually has probability zero. To say of an event that it is possible for it to occur is to say that its probability of occurring, however small, is non-zero. Saying that if a positive quantity is so small that we can't measure it then it is equal to zero, is saying that the quantity is at once positive and therefore non-zero and also equal to zero and therefore non-positive. Nothing can be both zero and positive because the definition of positivity is that the referent is strictly greater than zero and therefore strictly not equal to zero.