A Constructive Look at Functions of Bounded Variation
Douglas Bridges · Bulletin of the London Mathematical Society · 2000
Functions with bounded variation and with a (total) variation are examined within Bishop's constructive mathematics. It is shown that the property of having a variation is hereditary downward on compact intervals, and hence that a real-valued function f with a variation on a compact interval can be expressed as a difference of two increasing functions. Moreover, if f is sequentially continuous, then the corresponding variation function, and hence f itself, is uniformly continuous. 1991 Mathematics Subject Classification 26A45.