Subadditivity

"An outer measure μ ∗ {\displaystyle \mu ^{*}} satisfies a property called “subadditivity”, viz.: μ ∗ ( ⋃ j = 1 ∞ A j ) ≤ ∑ j = 1 ∞ μ ∗ ( A j ) {\displaystyle \mu ^{*}{\big (}\bigcup _{j=1}^{\infty }A_{j}{\big )}\leq \sum _{j=1}^{\infty }\mu ^{*}(A_{j})} . If the less-than-or-equal sign were replaced with an equal sign then the property would be “additivity” instead."