Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.
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4x8=8x4
That property is called CLOSURE.
3+3=6 3+3=6
Closure
Every subset of a frequent itemset is also frequent. Also known as Apriori Property or Downward Closure Property, this rule essentially says that we don't need to find the count of an itemset, if all its subsets are not frequent. This is made possible because of the anti-monotone property of support measure - the support for an itemset never exceeds the support for its subsets. Stay tuned for this.