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The counting measure of the empty set is 0, as there are no elements to count in an empty set.

The counting measure of a finite set is the number of elements in the set. For example, for the set {1, 2, 3}, the counting measure is 3.

Counting measure on a set is a measure that assigns to each subset of the set the number of elements in the subset, possibly infinity.

Counting measure is countably additive, meaning if you have a countable collection of disjoint sets, the measure of their union is the sum of their measures.

The counting measure of an infinite set is infinity ($\infty$) because the number of elements cannot be assigned a finite value.