In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function's values at each element.

What does Countably subadditive mean?

A set function is said to possess countable subadditivity if, given any countable disjoint collection of sets on which is defined, A function possessing countable subadditivity is said to be countably subadditive. Any countably subadditive function is also finitely subadditive presuming that where. is the empty set.

Are all measures subadditive?

A measure is an additive function, and, by definition, nowhere negative. So Additive Nowhere Negative Function is Subadditive‎ applies. Hence the result directly: μ(E∪F)≤μ(E)+μ(F)