Minkowski's Inequality establishes that the Lp spaces of mathematical analysis satisfy the triangle inequality required of a normed vector space, showing that the Lp norm of a sum of two functions is never more than the sum of their individual Lp norms. Named for the German mathematician Hermann Minkowski, it is one of the foundational inequalities underlying the theory of Lp spaces used throughout analysis.
Facts
StatementFor functions f and g belonging to an Lp space, the Lp norm of f + g is no greater than the sum of the Lp norms of f and g, so the Lp spaces satisfy the triangle inequality required of a normed vector space. 1 Classification
Statement Form Sources
1. Minkowski inequality, Wikipedia
IntroductionQuote, Introduction
establishes that the Lp spaces satisfy the triangle inequality in the definition of normed vector spaces
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