what is the finite variation function?

I am learning stochastic process for my research. However i am confused with the whole continuous - discontinuous thing.

The book im reading refers to something called the finite variation function, but i cant find much info on it on google. Does anyone know about this?

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Also there is a small derivation

if we define a discontinuous part gd of g as gd(t)

and the continuous part gc or g by gc(t) = g(t) - gd(t). It is clear gd only changes by jumps.

What is meant by this?

thank you for any help, this forum is a gold mine