Total variation of a function

The same as the variation of a function of one variable. The total variation of a real-valued function is the sum of its positive variation (cf. Positive variation of a function) and negative variation (cf. Negative variation of a function).

Comments

If is a complex-valued function on , then its total variation over is the number

If is also continuous, then this number is the same as the length of the arc in the complex plane that is parametrized by . If is absolutely continuous on , then

References

[a1]	K.R. Stromberg, "Introduction to classical real analysis" , Wadsworth (1981)