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Definition: Order Relation for Step Functions

Let \(\phi,\psi:[a,b]\mapsto\mathbb R\) be step functions over the closed interval \([a,b]\). The order relation for step functions is defined as \[\phi\le \psi:\Longleftrightarrow \phi(x)\le \psi(x)\quad\text{for all }x\in[a,b].\]

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983