in whether or not this given is the actual outcome of E; then we require that each singleton set {} belongs to F .

in whether or not this given ω is the actual outcome of E; then we require that each singleton set {ω} belongs to F . Let A ⊆ . Then A is countable (since  is countable), and so A may be expressed as the union of the countably many ωi which belong to A, giving that A =

S

ω∈A{ω} ∈ F by (1.4). The probability P(A) of the event A is determined by the collection of probabilities P({ω}) as ω ranges over , since, by (1.14), P(A) =

X

ω∈A P({ω}).