In mathematics, an F σ set (said F-sigma set) is a countable union of closed sets. The notation originated in French with F for fermé (French: closed) and σ for somme (French: sum, union). …

In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of …

In mathematics, given a positive or a signed measure on a measurable space , a -finite subset is a measurable subset which is the union of a countable number of measurable subsets of finite …

4 天之前 · A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for …

大多数情况下, X 应该是 Rn 中的一个开集 Ω, 我们首先要明确, 我们并不是要对每个函数都定义它的积分 (Riemann 积分理论中就有不可积分的函数) , 特别地, 对于 X 中的某个子集 A ⊂ X, 它的 …

Definition: A subset $F$ of $\mathbb{R}$ is an $F_{\sigma}$-set if $F$ is a countable union of closed sets. Note that each closed interval $[a, b] \subset \mathbb{R}$ is an $F_{\sigma}$ …

Let $\Omega \neq \emptyset$ be a set, $(\Xi, \Sigma)$ be a measure space and $f: \Omega \rightarrow \Xi$ a map. Define $\sigma(f) = \{f^{-1}(F): F \in \Sigma \}.$ Show that $\sigma(f)$ …

简单来说：就是把f(x)*f(y) 先对不同的y加一遍，再对不同的x加一遍 那这又是啥意思。 －－－－－－－－－－－－万能的分割 …

例：R^n中全体有理点集为F_sigma集。 例：f(x)是定义在开集上的实值函数，则f的连续点集是G_sigma集（函数连续点的结构）。 sigma代数 ，集合X中一些子集构成的集合族：满足

2019年7月10日 · Let $\mathcal{M}$ be a $\sigma$-algebra on $X$ such that $f$ is $\mathcal{M}/\mathcal{B}(\mathbb{R})$-measurable. By the very definition of measurability, it …