Riesz-Markov theorem says that space of Radon measures on [a,b] is isomorphic to linear functionals on $C[a,b]$ (continuous functions on $[a,b]$). On the other hand I am reading here https://www.math.cuhk.edu.hk/course_builder/2122/math4010/T3.pdf that dual space of $C[a,b]$ is space of right continuous functions with bounded variation which are $0$ in $a$.
Is everything okay?
Is space of right continuous functions with bounded variation which are $0$ in $a$ the same as space of Radon measures.
If yes how to see it?