Advanced Analytical Theory and Methods: Association Rules - Data Science and Big Data Analytics - page 194

If an itemset is considered frequent, then any subset of the frequent itemset must
also be frequent. This is referred to as the Apriori property (or downward
closure property ). For example, if 60% of the transactions contain
{bread,jam} , then at least 60% of all the transactions will contain {bread} or
{jam} . In other words, when the support of {bread,jam} is 0.6, the support of
{bread} or {jam} is at least 0.6. Figure 5.2 illustrates how the Apriori property
works. If itemset {B,C,D} is frequent, then all the subsets of this itemset, shaded,
must also be frequent itemsets. The Apriori property provides the basis for the
Apriori algorithm.
Figure 5.2 Itemset {A,B,C,D} and its subsets