On the Method of Inclusion and Exclusion
Lajos Takács · Journal of the American Statistical Association · 1967
Let Ω be an arbitrary set, , a σ-field of subsets of Ω, and V (A), a finite, countably additive set function defined on . Let A 1, A 2, · · ·, be a sequence of subsets of Ω belonging to . Denote by Hk , k = 0, 1, 2, · · ·, the set of elements of Ω which belong to exactly k sets among A 1, A 2, · · ·. In the theory of probability, in combinatorial analysis and in the theory of numbers there frequently arises the problem of finding V(Hk ), k = 0, 1, 2, · · ·. In this paper V(Hk ) is found if V(Ω) and V(Ai 1 Ai 2 · · · Ai r ), 1 ≤ i 1 < i 2< · · · < ir , are known.