|
It is shown that every probability measure μ on the interval [0, 1] gives rise to a unique infinite random graph g on vertices { v 1 , v 2 , . . .} and a sequence of random graphs gn on vertices { v 1 , . . . , v n } such that \( \mu (g_n \rightarrow g) \) . In particular, \( \mathbf{P}(G-n(Q)) \) for Bernoulli graphs with stable property Q , can be strengthened to: ∃ probability space (Ω, F, P ), ∃ set of infinite graphs G ( Q ) ∈, F with property Q such that \( P (G_n(Q) \rightarrow G(Q)) = 1 \quad \mathrm{and}\quad \mathbf{P}(G-n(Q)) = P(G_n(Q)) \) .
|
