n. a measurable space endowed with a non-negative measure. Any non-empty set, the collection of all its subsets, and the counting measure (the cardinality of these subsets) define a measure space. The measure is often desired to be positive except on the zero element, and this may be achieved by identifying sets with null symmetric difference; this done, the sets of finite measure in the resulting ring form a metric space in which the metric is given by the measure of the symmetric difference of two sets.