In mathematics, a Nikodym set is a subset of the unit square in with complement of Lebesgue measure zero, such that, given any point in the set, there is a straight line that only intersects the set at that point. The existence of a Nikodym set was first proved by Otto Nikodym in 1927. Subsequently, constructions were found of Nikodym sets having continuum many exceptional lines for each point, and Kenneth Falconer found analogues in higher dimensions. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets).
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| - Conjunto de Nikodym (es)
- Nikodym set (en)
- Множество Никодима (ru)
- Множина Нікодима (uk)
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| - En matemáticas, un conjunto de Nikodym es un conjunto N del cuadrado unidad S del plano euclídeo tal que
* la medida de Lebesgue de N es 1 y
* para cada punto x de N, existe una recta cuya intersección con N es únicamente x. La existencia de tal conjunto fue probada por primera vez por Nikodym en 1927. Los conjuntos de Nikodym están estrechamente relacionados con los (también conocidos como conjuntos de ). (es)
- Мно́жество Нико́дима — пример множества на плоскости, кажущийся парадоксальным с точки зрения теории меры. Этот пример тесно связан с множеством Безиковича. (ru)
- Множина Нікодима — приклад множини на площині, що здається парадоксальним з точки зору теорії міри. Цей приклад тісно пов'язаний з . (uk)
- In mathematics, a Nikodym set is a subset of the unit square in with complement of Lebesgue measure zero, such that, given any point in the set, there is a straight line that only intersects the set at that point. The existence of a Nikodym set was first proved by Otto Nikodym in 1927. Subsequently, constructions were found of Nikodym sets having continuum many exceptional lines for each point, and Kenneth Falconer found analogues in higher dimensions. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets). (en)
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| - En matemáticas, un conjunto de Nikodym es un conjunto N del cuadrado unidad S del plano euclídeo tal que
* la medida de Lebesgue de N es 1 y
* para cada punto x de N, existe una recta cuya intersección con N es únicamente x. La existencia de tal conjunto fue probada por primera vez por Nikodym en 1927. Los conjuntos de Nikodym están estrechamente relacionados con los (también conocidos como conjuntos de ). (es)
- In mathematics, a Nikodym set is a subset of the unit square in with complement of Lebesgue measure zero, such that, given any point in the set, there is a straight line that only intersects the set at that point. The existence of a Nikodym set was first proved by Otto Nikodym in 1927. Subsequently, constructions were found of Nikodym sets having continuum many exceptional lines for each point, and Kenneth Falconer found analogues in higher dimensions. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets). The existence of Nikodym sets is sometimes compared with the Banach–Tarski paradox. There is, however, an important difference between the two: the Banach–Tarski paradox relies on non-measurable sets. Mathematicians have also researched Nikodym sets over finite fields (as opposed to ). (en)
- Мно́жество Нико́дима — пример множества на плоскости, кажущийся парадоксальным с точки зрения теории меры. Этот пример тесно связан с множеством Безиковича. (ru)
- Множина Нікодима — приклад множини на площині, що здається парадоксальним з точки зору теорії міри. Цей приклад тісно пов'язаний з . (uk)
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