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Definition: Supremum Norm for Functions

Let $D$ be a set, $\mathbb F$ be a either the field of real numbers or the field of complex numbers and let $f:D\to\mathbb F$ be a function. We set $$||f||_\infty:=\sup\{|f(x)|\mid x\in D\},$$ where $|f(x)|$ is the absolute value of real numbers (or the absolute value of complex numbers) and call $||f||_\infty$ the supremum norm of $f$ on $D.$


| | | | | created: 2020-02-26 19:46:10 | modified: 2020-02-26 19:46:46 | by: bookofproofs | references: [581]

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983