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How can we define L-Infinity Norm for the multi-variable function?

For $$ \|f(t,x_1,\cdots,x_n)\|_\infty = ?$$ where $f \in C^\infty ([0,\infty) \times \mathbb R^n) $.

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    Would you not define it basically the same way you define regular old $L^{\infty}(\mathbb{R})$ (the essential supremum)?2012-04-21
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    What happens if $f$ is not bounded?2012-04-21

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