ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4728 on D379: Maximum operation
Formulation 0
Let $x_1, \ldots, x_N \in \mathbb{R}^D$ each be a D4924: Euclidean real number.
Let $p \in (0, \infty)$ be a D5407: Positive real number.
Then \begin{equation} \sum_{n = 1}^N |x_n| \leq N \left( \sum_{n = 1}^N |x_n|^p \right)^{1 / p} \end{equation}