Definition: Positive and Negative Parts of a Real-Valued Function

Let $D$ be a real interval and $f:D\to\mathbb R$ a function. Using the order-relation for real numbers, we define:

Note that $f_+\ge 0$ and $f_-\ge 0$ and that $f=f_+-f_-$ as well as $|f|=f_++f_-.$

Propositions: 1


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References

Bibliography

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