About: Rademacher's theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Rademacher's theorem Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Theorem106752293, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FRademacher%27s_theorem&invfp=IFP_OFF&sas=SAME_AS_OFF

In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn and f: U → Rm is Lipschitz continuous, then f is differentiable almost everywhere in U; that is, the points in U at which f is not differentiable form a set of Lebesgue measure zero. Differentiability here refers to infinitesimal approximability by a linear map, which in particular asserts the existence of the coordinate-wise partial derivatives.

Attributes	Values
rdf:type	yago:WikicatMathematicalTheorems yago:WikicatTheoremsInAnalysis yago:WikicatTheoremsInMeasureTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 programming language yago:Statement106722453 yago:Theorem106752293
rdfs:label	Teorema de Rademacher (ca) Satz von Rademacher (de) Théorème de Rademacher (fr) Teorema di Rademacher (it) ラーデマッヘルの定理 (ja) Twierdzenie Rademachera (pl) Stelling van Rademacher (nl) Rademacher's theorem (en) Теорема Радемахера (ru) Теорема Радемахера (uk)
rdfs:comment	En anàlisi matemàtica, el teorema de Rademacher, que du el nom de Hans Rademacher, afirma que si U és un subconjunt obert de Rn i f: U → Rm és Lipschitz contínua, llavors f és diferenciables gairebé pertot en U; és a dir, els punts en U en què f no és diferenciable formen un conjunt amb mesura de Lebesgue zero. (ca) Der Satz von Rademacher, benannt nach dem deutschen Mathematiker Hans Rademacher, ist ein Satz der Analysis über Lipschitz-stetige Funktionen. (de) In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn and f: U → Rm is Lipschitz continuous, then f is differentiable almost everywhere in U; that is, the points in U at which f is not differentiable form a set of Lebesgue measure zero. Differentiability here refers to infinitesimal approximability by a linear map, which in particular asserts the existence of the coordinate-wise partial derivatives. (en) 数学の解析学の分野におけるラーデマッヘルの定理（ラーデマッヘルのていり、英: Rademacher's theorem）とは、ハンス・ラーデマッヘルの名にちなむ、次の定理のことを言う：U を Rn 内のある開部分集合とし、関数 f : U → Rm はリプシッツ連続であるとする。このとき、f は U 内のほとんど至る所でフレシェ微分可能である。すなわち、f が微分可能ではないような U 内の点からなる集合は、そのルベーグ測度がゼロである。 (ja) In analisi matematica, il teorema di Rademacher afferma che, se è un sottoinsieme aperto di e una funzione lipschitziana, allora è differenziabile quasi ovunque in , ovvero i punti in cui non è differenziabile formano un insieme di misura nulla. (it) In de wiskundige analyse stelt de stelling van Rademacher, genoemd naar de Duitse wiskundige Hans Rademacher, het volgende: Als een open deelverzameling van is en tevens geldt dat Lipschitz-continu is, dan is bijna overal in Fréchet-differentieerbaar (dat wil zeggen dat de punten in , waar niet differentieerbaar zijn een verzameling vormen met Lebesgue-maat nul). (nl) Twierdzenia Rademachera – twierdzenie mówiące od różniczkowalności prawie wszędzie funkcji wielu zmiennych, spełniających warunek Lipschitza. Twierdzenie zostało po raz pierwszy sformułowane i udowodnione w 1919. (pl) Теорема Радемахера — классическая теорема в теории функции вещественной переменной. (ru) В математичному аналізі, теорема Радемахера, названа на честь , стверджує, що якщо U — відкрита множина і — відображення Ліпшиця, то f є диференційованим майже всюди на U (тобто точки U в яких f не є диференційоване утворюють множину міра Лебега якої рівна нулю). (uk) En mathématiques, le théorème de Rademacher est un résultat d'analyse qui s'énonce ainsi : Soient A un ouvert de ℝn et f : A → ℝm une application lipschitzienne. Alors f est dérivable presque partout sur A. (fr)
dcterms:subject	Theorems in measure theory Lipschitz maps
Wikipage page ID	7764195 (xsd:integer)
Wikipage revision ID	1119370246 (xsd:integer)
Link from a Wikipage to another Wikipage	Metric differential Normal vector Bounded variation Almost everywhere Approximate limit Dominated convergence theorem Mathematical analysis Geometric measure theory Alexandrov theorem Theorems in measure theory Lipschitz continuity Sobolev space Fundamental lemma of calculus of variations Mathematische Annalen CRC Press Lebesgue differentiation theorem Lebesgue measure Alberto Calderón Curvature Euclidean space Difference quotient Graduate Texts in Mathematics Hans Rademacher Chain rule Rectifiable set Dot product Convexity McGraw-Hill Book Co. Metric space Open set Lipschitz maps John Wiley & Sons, Inc. Pansu derivative Fubini theorem Springer-Verlag Tangent plane Charles Morrey Sobolev embedding theorem Generalized derivative
Link from a Wikipage to an external page	http://www.math.jyu.fi/research/reports/rep100.pdf%23page=18 https://web.stanford.edu/class/math285/ts-gmt.pdf%7Czbl=0546.49019
sameAs	Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem Rademacher's theorem
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Cite_web dbt:Math dbt:Mvar dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfnm
3loc	Chapter 7 (en) Theorem 10.8 (en)

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software