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- Minkowski_inequality abstract "In mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. Let S be a measure space, let 1 ≤ p ≤ ∞ and let f and g be elements of Lp(S). Then f + g is in Lp(S), and we have the triangle inequalitywith equality for 1 < p < ∞ if and only if f and g are positively linearly dependent,i.e., f = g for some ≥ 0. Here, the norm is given by:if p < ∞, or in the case p = ∞ by the essential supremumThe Minkowski inequality is the triangle inequality in Lp(S). In fact, it is a special case of the more general factwhere it is easy to see that the right-hand side satisfies the triangular inequality.Like Hölder's inequality, the Minkowski inequality can be specialized to sequences and vectors by using the counting measure:for all real (or complex) numbers x1, ..., xn, y1, ..., yn and where n is the cardinality of S (the number of elements in S).".
- Minkowski_inequality wikiPageExternalLink ?1mw1tkgozzu.
- Minkowski_inequality wikiPageID "192022".
- Minkowski_inequality wikiPageRevisionID "594797676".
- Minkowski_inequality author "M.I. Voitsekhovskii".
- Minkowski_inequality hasPhotoCollection Minkowski_inequality.
- Minkowski_inequality id "M/m064060".
- Minkowski_inequality title "Minkowski inequality".
- Minkowski_inequality subject Category:Articles_containing_proofs.
- Minkowski_inequality subject Category:Inequalities.
- Minkowski_inequality type Abstraction100002137.
- Minkowski_inequality type Attribute100024264.
- Minkowski_inequality type Difference104748836.
- Minkowski_inequality type Inequalities.
- Minkowski_inequality type Inequality104752221.
- Minkowski_inequality type Quality104723816.
- Minkowski_inequality comment "In mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. Let S be a measure space, let 1 ≤ p ≤ ∞ and let f and g be elements of Lp(S). Then f + g is in Lp(S), and we have the triangle inequalitywith equality for 1 < p < ∞ if and only if f and g are positively linearly dependent,i.e., f = g for some ≥ 0.".
- Minkowski_inequality label "Desigualdad de Minkowski".
- Minkowski_inequality label "Desigualdade de Minkowski".
- Minkowski_inequality label "Disuguaglianza di Minkowski".
- Minkowski_inequality label "Inégalité de Minkowski".
- Minkowski_inequality label "Minkowski inequality".
- Minkowski_inequality label "Minkowski-Ungleichung".
- Minkowski_inequality label "Nierówność Minkowskiego".
- Minkowski_inequality label "Неравенство Минковского".
- Minkowski_inequality label "ミンコフスキーの不等式".
- Minkowski_inequality label "闵可夫斯基不等式".
- Minkowski_inequality sameAs Minkowského_nerovnost.
- Minkowski_inequality sameAs Minkowski-Ungleichung.
- Minkowski_inequality sameAs Desigualdad_de_Minkowski.
- Minkowski_inequality sameAs Minkowskiren_desberdintza.
- Minkowski_inequality sameAs Inégalité_de_Minkowski.
- Minkowski_inequality sameAs Disuguaglianza_di_Minkowski.
- Minkowski_inequality sameAs ミンコフスキーの不等式.
- Minkowski_inequality sameAs 민코프스키_부등식.
- Minkowski_inequality sameAs Nierówność_Minkowskiego.
- Minkowski_inequality sameAs Desigualdade_de_Minkowski.
- Minkowski_inequality sameAs m.01b84q.
- Minkowski_inequality sameAs Q755092.
- Minkowski_inequality sameAs Q755092.
- Minkowski_inequality sameAs Minkowski_inequality.
- Minkowski_inequality wasDerivedFrom Minkowski_inequality?oldid=594797676.
- Minkowski_inequality isPrimaryTopicOf Minkowski_inequality.