  A functional calculus for an order complete vector lattice $\mathcal{E}$ was
developed by Grobler in 2014 using the Daniell integral. We show that if one
represents the universal completion of $\mathcal{E}$ as $C^\infty(K)$, then the
Daniell functional calculus for continuous functions is exactly the pointwise
composition of functions in $C^\infty(K)$. This representation allows an easy
deduction of the various properties of the functional calculus. Afterwards, we
study discrete stopping times and stopped processes in $C^\infty(K)$. We obtain
a representation that is analogous to what is expected in probability theory.
