§8.3 Absolutely Continuous Functions

Theorem 1. Let F ,G be a functions on a cell K such that G is of bounded variation on K and

(i) f A dF —> 0 for every sequence A i, A 2 , · · · of figures in K such that

Then F is of bounded variation on K and (ii) f A \dF\ —> 0 for every sequence A \, A2,··· of figures

in K for which (1 ) holds.