= Probability measure
{wiki}
A probability measure is a nonnegative, <countably additive> <measure> with total mass one. Thus $\mathbb P(\Omega)=1$, and for pairwise <disjoint events> $A_j$,
$$
\mathbb P\left(\bigcup_{j=1}^{\infty}A_j\right)=\sum_{j=1}^{\infty}\mathbb P(A_j).
$$
The <complement of an event> has <probability> $1-\mathbb P(A)$. The <probability> of a <union> of overlapping <events> needs a correction: $\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)$. Counting the overlap once is the simplest instance of the <inclusion-exclusion principle>.
A <zero-probability event> need not be impossible as a member of the <sample space>. Under the <continuous uniform distribution> on $[0,1]$, every individual point has <probability> zero, while the whole interval has <probability> one. <Countable additivity> applies to countable <unions>, not arbitrary uncountable ones; there is no contradiction.
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