Subadditivity

An outer measure μ^* satisfies a property called “subadditivity”, viz.: μ^* big (∪ⱼ₌₁ ᪲A_j big )<∑ⱼ₌₁ ᪲μ^*(A_j). If the less-than-or-equal sign were replaced with an equal sign then the property would be “additivity” instead.