 Layer cake representation

For a nonnegative measurable function $g$,On a graph, applying this identity to $|g(x)-g(y)|$ expresses its total variation as the integral of the edge boundaries of the superlevel sets.

More generally, if $\phi :[0,\infty )\to [0,\infty )$ is differentiable, increasing, and satisfies $\phi (0)=0$, then Tonelli theorem and the fundamental theorem of calculus give

Layer cake representation is a concept often used in various fields, including geography, data visualization, and computer science, to illustrate the arrangement of different layers or components in a structured way. The term is commonly associated with two main contexts: 1. **Geology and Geography**: In this context, a layer cake representation illustrates the stratification of geological layers. Each "layer" represents different materials, sediments, or rock formations that have accumulated over time.