To every $f$ there correspond two functions $a$ and $b$.
Consider the differences between these integrals and the corresponding ones with $f$ replaced by $g$.
Let $v$ be an arbitrary control and $x_t$ the corresponding controlled process. [Not: “the respective process”; “respective” requires a plural noun.]
It seems appropriate to mention in passing the corresponding formula for the cohomology of $B_n$.
Corresponding to each choice of $V$ there is a function $f$ such that ......