Let $X$ and $\widehat{X}$ be a pair of dual standard Markov processes. We associate to each exact multiplicative function $\left(MF\right)$, $M$ of $X$ a unique exact $MF$, $\widehat{M}$ of $\widehat{X}$ in a natural manner. Any $MF$, $M$ is assumed to satisfy $0\le M_t\le 1$. The map $M\to \widehat{M}$ is bijective and multiplicative in the sense that: $(MN{)}^{\wedge }=\widehat{M}\widehat{N}$.This correspondence is studied in some detail and several important examples are discussed.These results are then applied to study additive functionals.