ABSTRACT

Theorem 1 (§5.3) yields the following version of the Funda­ mental Theorem of Calculus.

T heorem 1 . Let σ = [S'] and r — [T] be differentials on a cell K such that σ is continuous wherever it is either left or right continuous, and |σ| is dampable. Let f be a function on K . Then (i) is equivalent to (ii):

(ii) Every σ -null set is τ -null, and for σ -all t in K the fol­ lowing condition holds:

(i)

(1) As (I, t ) —► t, S (I, t) φ 0 ultimately and ^ —> f( t) .