Editing Probability space (section)

== General case ==

If {{math|Ω}} is [[uncountable set|uncountable]], still, it may happen that {{math|''P''(''ω'') ≠ 0}} for some {{math|''ω''}}; such {{math|''ω''}} are called [[atom (measure theory)|atom]]s. They are an at most countable (maybe [[empty set|empty]]) set, whose probability is the sum of probabilities of all atoms. If this sum is equal to 1 then all other points can safely be excluded from the sample space, returning us to the discrete case. Otherwise, if the sum of probabilities of all atoms is between 0 and 1, then the probability space decomposes into a discrete (atomic) part (maybe empty) and a [[atom (measure theory)|non-atomic]] part.