Page "Ultrafilter" Paragraph 0

In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged ( as a filter ).

An ultrafilter may be considered as a finitely additive measure.

Then every subset of X is either considered " almost everything " ( has measure 1 ) or " almost nothing " ( has measure 0 ).

If A is a subset of X, then either A or X