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A set function mu possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

For a countable set of n disjoint events E_1, E_2, ..., E_n P( union _(i=1)^nE_i)=sum_(i=1)^nP(E_i).

Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess countable monotonicity provided that, whenever a set E in S is covered by ...

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

A positive integer: 1, 2, 3, 4, ... (OEIS A000027), also called a natural number. However, zero (0) is sometimes also included in the list of counting numbers. Due to lack of ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...