§2.7 Functions as Differential Coefficients

For σ a differential and / a function on a cell K we have defined

(1)

in (3) of §2.1. For f S to be a viable summant the function / must be defined and finite everywhere on K. But we want to relax this restriction on the differential coefficient / in the differential fa . Specifically we demand only that / be defined and finite “σ-everywhere” on K . We introduce this concept as follows.