Is the triangle inequality also true for functions? if so why? my confusion comes from that sup of the sum of two sets is different from supremum of the sum of 2 functions.
2026-03-26 18:49:42.1774550982
Triangle inequality for functions.
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The triangle inequality is a property of a normed vector space (by definition). So you can't ask this question about "functions" in general, but about a particular choice of function space and candidate norm. The very common $L^p$ spaces do satisfy the triangle inequality for $p > 1$, including the supremum case $p=\infty$ (this is Minkowski's inequality.)