Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1302-0677-2 |
Объём: | 68 страниц |
Масса: | 123 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
In mathematics, more specifically in measure theory, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area and volume of Euclidean geometry to suitable subsets of Rn, n=1,2,3,.... For instance, the Lebesgue measure of [0,1] in the real numbers is its length in the non-formal sense of the word, specifically 1. To qualify as a measure (see Definition below), a function that assigns a non-negative real number or infinity to a set's subsets must satisfy a few conditions. One important condition is countable additivity. This condition states that the size of the union of a sequence of disjoint subsets is equal to the sum of the sizes of the subsets. However, it is in general impossible to consistently associate a size to each subset of a given set and also satisfy the other axioms of a measure.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.