## Introduction on total variation of functions

Recall that a function of **bounded variation**, also known as a **BV-function**, is a real-valued function whose **total variation** is bounded (finite).

Being more formal, the **total variation** of a real-valued function \(f\), defined on an interval \([a,b] \subset \mathbb{R}\) is the quantity:

\[V_a^b(f) = \sup\limits_{P \in \mathcal{P}} \sum_{i=0}^{n_P-1} \left\vert f(x_{i+1}) – f(x_i) \right\vert\] where the **supremum** is taken over the set \(\mathcal{P}\) of all **partitions of the interval** considered. Continue reading A continuous function which is not of bounded variation