. . "5077"^^ . . . "\u041B\u0435\u043C\u043C\u0430 \u0411\u0435\u0437\u0438\u043A\u043E\u0432\u0438\u0447\u0430 \u043E \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u044F\u0445"@ru . "\u30D9\u30B7\u30B3\u30D3\u30C3\u30C1\u306E\u88AB\u8986\u5B9A\u7406 (\u30D9\u30B7\u30B3\u30D3\u30C3\u30C1\u306E\u3072\u3075\u304F\u3066\u3044\u308A, Besicovitch covering lemma)\u3068\u306F\u3001\u6B21\u5143\u306B\u306E\u307F\u4F9D\u5B58\u3059\u308B\u5B9A\u6570\u306B\u3088\u3063\u3066\u6210\u308A\u7ACB\u3064\u88AB\u8986\u306B\u95A2\u3059\u308B\u5B9A\u7406\u3067\u3001\u5E7E\u4F55\u5B66\u7684\u6E2C\u5EA6\u8AD6\u306A\u3069\u306E\u5B9F\u89E3\u6790\u306E\u5206\u91CE\u3067\u4F7F\u308F\u308C\u308B\u3002"@ja . "\u6578\u5B78\u4E0A\uFF0C\u8C9D\u897F\u79D1\u7DAD\u5947(Besicovitch)\u8986\u84CB\u5B9A\u7406\u662F\u5BE6\u5206\u6790\u7684\u4E00\u689D\u8986\u84CB\u5B9A\u7406\u3002\u6B50\u6C0F\u7A7A\u9593\u7684\u4EFB\u4F55\u4E00\u500B\u6709\u534A\u5F91\u4E0A\u9650\u7684\u9589\u7403\u65CF\u4E2D\uFF0C\u53EF\u4EE5\u53D6\u51FA\u5E7E\u500B\u5B50\u96C6\uFF0C\u5B50\u96C6\u7684\u7403\u4E92\u4E0D\u76F8\u4EA4\uFF0C\u4E14\u8986\u84CB\u539F\u4F86\u9589\u7403\u65CF\u4E2D\u6240\u6709\u7403\u7684\u4E2D\u5FC3\uFF0C\u800C\u5B50\u96C6\u7684\u6578\u76EE\u4E0A\u9650\u53EA\u53D6\u6C7A\u65BC\u7A7A\u9593\u7684\u7DAD\u6578\u3002"@zh . "\u041B\u0435\u043C\u043C\u0430 \u0411\u0435\u0437\u0438\u043A\u043E\u0432\u0438\u0447\u0430 \u043E \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u044F\u0445 \u2014 \u043A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 \u0432\u0430\u0436\u043D\u044B\u0439 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u043C\u0435\u0440\u044B \u0438 \u0431\u043B\u0438\u0437\u043A\u0438\u0439 \u043A \u043B\u0435\u043C\u043C\u0435 \u0412\u0438\u0442\u0430\u043B\u0438. \u0414\u043E\u043A\u0430\u0437\u0430\u043D\u0430 \u0411\u0435\u0437\u0438\u043A\u043E\u0432\u0438\u0447\u0435\u043C \u0432 1945-\u043C \u0433\u043E\u0434\u0443."@ru . "17743903"^^ . "In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover. The Besicovitch covering theorem asserts that there exists a constant cN depending only on the dimension N with the following property: \n* Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1\u2009=\u2009{Bn1}, \u2026, AcN\u2009=\u2009{BncN} contained in F such that each collection Ai consists of disjoint balls, and Let G denote the subcollection of F consisting of all balls from the cN disjoint families A1,...,AcN.The less precise following statement is clearly true: every point x\u2009\u2208\u2009RN belongs to at most cN different balls from the subcollection G, and G remains a cover for E (every point y\u2009\u2208\u2009E belongs to at least one ball from the subcollection G). This property gives actually an equivalent form for the theorem (except for the value of the constant). \n* There exists a constant bN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there is a subcollection G of F such that G is a cover of the set E and every point x\u2009\u2208\u2009E belongs to at most bN different balls from the subcover G. In other words, the function SG equal to the sum of the indicator functions of the balls in G is larger than 1E and bounded on RN by the constant bN,"@en . "In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover. The Besicovitch covering theorem asserts that there exists a constant cN depending only on the dimension N with the following property: \n* Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1\u2009=\u2009{Bn1}, \u2026, AcN\u2009=\u2009{BncN} contained in F such that each collection Ai consists of disjoint balls, and"@en . "Besicovitch covering theorem"@en . "\u30D9\u30B7\u30B3\u30D3\u30C3\u30C1\u306E\u88AB\u8986\u5B9A\u7406"@ja . . "Twierdzenie Besicovitcha o pokryciu"@pl . . . . . . . "860208702"^^ . . . . . . "\u041B\u0435\u043C\u043C\u0430 \u0411\u0435\u0437\u0438\u043A\u043E\u0432\u0438\u0447\u0430 \u043E \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u044F\u0445 \u2014 \u043A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 \u0432\u0430\u0436\u043D\u044B\u0439 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u043C\u0435\u0440\u044B \u0438 \u0431\u043B\u0438\u0437\u043A\u0438\u0439 \u043A \u043B\u0435\u043C\u043C\u0435 \u0412\u0438\u0442\u0430\u043B\u0438. \u0414\u043E\u043A\u0430\u0437\u0430\u043D\u0430 \u0411\u0435\u0437\u0438\u043A\u043E\u0432\u0438\u0447\u0435\u043C \u0432 1945-\u043C \u0433\u043E\u0434\u0443."@ru . . . . . . . "\u30D9\u30B7\u30B3\u30D3\u30C3\u30C1\u306E\u88AB\u8986\u5B9A\u7406 (\u30D9\u30B7\u30B3\u30D3\u30C3\u30C1\u306E\u3072\u3075\u304F\u3066\u3044\u308A, Besicovitch covering lemma)\u3068\u306F\u3001\u6B21\u5143\u306B\u306E\u307F\u4F9D\u5B58\u3059\u308B\u5B9A\u6570\u306B\u3088\u3063\u3066\u6210\u308A\u7ACB\u3064\u88AB\u8986\u306B\u95A2\u3059\u308B\u5B9A\u7406\u3067\u3001\u5E7E\u4F55\u5B66\u7684\u6E2C\u5EA6\u8AD6\u306A\u3069\u306E\u5B9F\u89E3\u6790\u306E\u5206\u91CE\u3067\u4F7F\u308F\u308C\u308B\u3002"@ja . . . . . "\u6578\u5B78\u4E0A\uFF0C\u8C9D\u897F\u79D1\u7DAD\u5947(Besicovitch)\u8986\u84CB\u5B9A\u7406\u662F\u5BE6\u5206\u6790\u7684\u4E00\u689D\u8986\u84CB\u5B9A\u7406\u3002\u6B50\u6C0F\u7A7A\u9593\u7684\u4EFB\u4F55\u4E00\u500B\u6709\u534A\u5F91\u4E0A\u9650\u7684\u9589\u7403\u65CF\u4E2D\uFF0C\u53EF\u4EE5\u53D6\u51FA\u5E7E\u500B\u5B50\u96C6\uFF0C\u5B50\u96C6\u7684\u7403\u4E92\u4E0D\u76F8\u4EA4\uFF0C\u4E14\u8986\u84CB\u539F\u4F86\u9589\u7403\u65CF\u4E2D\u6240\u6709\u7403\u7684\u4E2D\u5FC3\uFF0C\u800C\u5B50\u96C6\u7684\u6578\u76EE\u4E0A\u9650\u53EA\u53D6\u6C7A\u65BC\u7A7A\u9593\u7684\u7DAD\u6578\u3002"@zh . . . . . . . . . "Twierdzenie Besicovitcha o pokryciu \u2013 jedno z dw\u00F3ch podstawowych twierdze\u0144 o pokryciu nosz\u0105ce nazwisko Abrama Besicovitcha, uog\u00F3lnienie twierdzenia Vitalego na og\u00F3lniejsze miary Radona na przestrzeniach euklidesowych; z geometrycznego punktu widzenia twierdzenie Vitalego daje pokrycie kulami powi\u0119kszonymi w stosunku do wyj\u015Bciowych, z kolei twierdzenie Besicovitcha wykorzystuje kule pokrycia wyj\u015Bciowego kosztem pewnego kontrolowanego nak\u0142adania si\u0119 kul. Zasadniczym zastosowaniem twierdzenia jest wykorzystanie w dowodzie (dzi\u0119ki mo\u017Cliwo\u015Bci \u201Ewype\u0142nienia\u201D dowolnego zbioru otwartego przeliczaln\u0105 rodzin\u0105 kul (parami) roz\u0142\u0105cznych w taki spos\u00F3b, \u017Ce pozosta\u0142a niewype\u0142niona cz\u0119\u015B\u0107 jest miary zero), a dzi\u0119ki temu twierdzenia Lebesgue\u2019a o punktach g\u0119sto\u015Bci dla miar Radona."@pl . . . . . "Twierdzenie Besicovitcha o pokryciu \u2013 jedno z dw\u00F3ch podstawowych twierdze\u0144 o pokryciu nosz\u0105ce nazwisko Abrama Besicovitcha, uog\u00F3lnienie twierdzenia Vitalego na og\u00F3lniejsze miary Radona na przestrzeniach euklidesowych; z geometrycznego punktu widzenia twierdzenie Vitalego daje pokrycie kulami powi\u0119kszonymi w stosunku do wyj\u015Bciowych, z kolei twierdzenie Besicovitcha wykorzystuje kule pokrycia wyj\u015Bciowego kosztem pewnego kontrolowanego nak\u0142adania si\u0119 kul."@pl . "\u8C9D\u897F\u79D1\u7DAD\u5947\u8986\u84CB\u5B9A\u7406"@zh .