Mutual Independence

Definition

A collection of elements $A_1,\dots ,A_n$ is mutually independent if for any sub-collection $A_k,\dots ,A_j$ $P(A_k\cap A_{k+1}\cap \cdots \cap A_j)=P(A_k)P(A_{k+1})\dots P(A_j)⟺P({\cap }_{i=1}^m{A}_{k_i})={\Pi }_{i=1}^{m}P(A_{k_i})$