 In a similar manner, every Radon measure μ on "U" defines an element of D′("U") whose value on the test function "formula_1" is ∫"formula_1" "dμ".As above, it is conventional to abuse notation and write the pairing between a Radon measure "μ" and a test function "formula_1" as formula_304.Conversely, as shown in a theorem by Schwartz (similar to the Riesz representation theorem), every distribution which is non-negative on non-negative functions is of this form for some (positive) Radon measure.