 and any representation theorem about the dual space of "X" may, through the transpose formula_268, be transferred directly to elements of the space formula_269.The natural inclusion formula_270 is a continuous injection whose image is dense in its codomain, so the transpose formula_271 is also a continuous injection.Note that the continuous dual space formula_272 can be identified as the space of Radon measures, where there is a one-to-one correspondence between the continuous linear functionals formula_273 and integral with respect to a Radon measure; 
that is, 
Through the injection formula_282, every Radon measure becomes a distribution on "U".