 If μ is absolutely continuous with respect to Lebesgue measure with density "f" and "d"μ = "f" "dx", then this definition for "R"μ is the same as the previous one for "Tf", but if μ is not absolutely continuous, then "R"μ is a distribution that is not associated with a function.For example, if "P" is the point-mass measure on R that assigns measure one to the singleton set {0} and measure zero to sets that do not contain zero, then

so that "R""P" = "δ" is the Dirac delta.Distributions may be multiplied by real numbers and added together, so they form a real vector space.