Editing Distribution (mathematics) (section)

====Positive Radon measures====

A linear function <math>T</math> on a space of functions is called '''{{em|positive}}''' if whenever a function <math>f</math> that belongs to the domain of <math>T</math> is non-negative (that is, <math>f</math> is real-valued and <math>f \geq 0</math>) then <math>T(f) \geq 0.</math> One may show that every positive linear functional on <math>C_c^0(U)</math> is necessarily continuous (that is, necessarily a Radon measure).{{sfn|Trèves|2006|p=218}} 
[[Lebesgue measure]] is an example of a positive Radon measure.