Whitney covering lemma

Whitney covering lemma

In mathematical analysis, the Whitney covering lemma is a lemma which asserts the existence of a certain type of partition of an open set in a Euclidean space. Originally it was employed in the proof of Hassler Whitney's extension theorem. The lemma was subsequently applied to prove generalizations of the Calderón-Zygmund decomposition.

Roughly speaking, the lemma states that it is possible to cover an open set by cubes each of whose diameter is proportional, within certain bounds, to its distance from the boundary of the open set. More precisely,

* An open subset "A" of R"n" can be written as a disjoint union of countably many closed cubes {"Q"j} whose corners have dyadic rational coordinates such that the following inequality holds for all "j" ∈ N:::mathrm{diam}(Q_j) le ext{dist}(Q_j, partial A)le 4 ext{diam}(Q_j).

References

*.
*.
*.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • List of mathematics articles (W) — NOTOC Wad Wadge hierarchy Wagstaff prime Wald test Wald Wolfowitz runs test Wald s equation Waldhausen category Wall Sun Sun prime Wallenius noncentral hypergeometric distribution Wallis product Wallman compactification Wallpaper group Walrasian… …   Wikipedia

  • Dyadic cubes — In mathematics, the dyadic cubes are a collection of cubes in ℝn of different sizes or scales such that the set of cubes of each scale partition ℝn and each cube in one scale may be written as a union of cubes of a smaller scale. These are… …   Wikipedia

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • Séminaire Nicolas Bourbaki (1950–1959) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s. 1950/51 series *33 Armand Borel, Sous groupes compacts maximaux des groupes de Lie, d après Cartan, Iwasawa et Mostow (maximal compact subgroups) *34 Henri Cartan, Espaces… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”