> The well-known definition of bounded variation functions is about
> their behavior on closed intervals.
> To say, "The total variation of real-valued function f, defined on an
> interval [a, b] belongs to R is the quantity V_a_b_(f) = sup(sum(|f(x_i
> +1) - f(x_i)|)) of all partitions of the interval considered", (etc.)

> My question is, can I use or define total variation for a half-open
> interval, say, [a, b)?

> In any case, my intention is to define (or use) the following: for any
> eps > 0 the total variation of the function
> f on the interval [a, b - eps] is finite. Is it the same as to say
> that the total variation of a function over the half-open interval [a,
> b) is finite?

> Regards,
> Miki