Category:Variation of Real Function

This category contains results about Variation of Real Function.
Definitions specific to this category can be found in Definitions/Variation of Real Function.

Let $f: \R \to \R$ be a real function whose domain is the closed real interval $\closedint a b$.

The variation of $f$ is defined as:

$\ds \map \sup {\sum_{i \mathop = 1}^n \size {\map f {x_i} - \map f {x_{i - 1} } } }$

where the supremum is taken over all possible finite subdivisions $a = x_0 < x_1 < x_2 < \cdots < x_n = b$ of $\closedint a b$.