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{title2=$V_a^b(f)$}
{wiki=Total_variation}

The total variation of $f:[a,b]\to\mathbb R$ is
$$
V_a^b(f)=\sup_{a=t_0<\cdots<t_n=b}
\sum_{k=1}^n|f(t_k)-f(t_{k-1})|.
$$
The function has bounded variation when this quantity is finite.

Total variation of a function

Finite-variation process

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 202 / 3 / b / Solution

Total variation of a function ( $V_{a}^{b} (f)$ )

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Total variation of a function (Vab​(f))

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