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独孤九剑
- 自我介绍
“独孤九剑”的要旨,在于一眼见到对方招式中的破绽,便即乘虚而入,后发先至,一招制胜,
群组: 南京邮电大学数模协会 群组: 数学散仙 群组: 数模应用 群组: 数学趣味、游戏、IQ等 群组: 2011年第一期数学建模 |
数学上,测度(Measure)是一个函数,它对一个给定集合的某些子集指定一个数,这个数可以比作大小、体积、概率等等。传统的积分是在区间上进行的,后来人们希望把积分推广到任意的集合上,就发展出测度的概念,它在数学分析和概率论有重要的地位。
In mathematics, more specifically measure theory, a measure is intuitively a certain association between subsets of a given set X and the (extended set) of non-negative real numbers. Often, some subsets of a given set X are not required to be associated to a non-negative real number; the subsets which are required to be associated to a non-negative real number are known as the measurable subsets of X. The collection of all measurable subsets of X is required to form what is known as a sigma algebra; namely, a sigma algebra is a subcollection of the collection of all subsets of X that in addition, satisfies certain axioms.
Measures can be thought of as a generalization of the notions: 'length,' 'area' and 'volume.' The Lebesgue measure defines this for subsets of a Euclidean space, and an arbitrary measure generalizes this notion to subsets of any set. The original intent for measure was to define the Lebesgue integral, which increases the set of integrable functions considerably. It has since found numerous applications in probability theory, in addition to several other areas of academia, particularly in mathematical analysis. There is a related notion of volume form used in differential topology. |
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