我们可以根据\mathcal{F}中所含的信息来判断事件A是否发生;类似的,E(X|\mathcal{F})即为根据我们所掌握的信息对X的值进行的最佳猜测(best guess),可与随机猜测作对应,随机猜测即类似于对X的值进行随机化选取(猜测),以下给出一些具体例子辅助理解此物理意义,这些例子来源于Durrett等人的教材:Probability: Theory...
（这里注意哦，这个集合的每个元素也是集合哦，所以描述中直接写1，2，3，4 是不对的，应该是{1},{2},{3}等ʕ⁎̯͡⁎ʔ༄），并且它需要满足以下三点特性（也就是必须是σ－field）：Φ∈F（也就是必须包含不可能事件）如果E∈F,Ec∈F。如果E1,E2,...,Ei∈F,那么Ui=1∞Ei∈F（似乎...
In this paper we consider fuzzy probabilities constructed over fuzzy topological spaces. We also extend the results to product fuzzy topological space with product fuzzy topological space. The theory can be considered to be an extension from the crisp cases to fuzzy cases.关键词: Fuzzy probability ...
There are many ideas from set theory that undergird probability. One such idea is that of a sigma-field. A sigma-field refers to the collection of subsets of asample spacethat we should use in order to establish a mathematically formal definition of probability. The sets in the sigma-field...
A notion of relaxed conditional expectation with respect to it relaxed sigma -field is identified. The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional expectation operator is continuous on the completion of the space. Other properties of ...
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The first thing you should see here is that the normal probability plot doesn’t appear to be normally distributed (a straight line), which is a requirement. The histogram confirms that since it does not appear symmetrical around a center value. And finally…bunnies in the clouds? Those graph...
On the Borel $\\sigma $-field and the Baire property 来自 ResearchGate 喜欢 0 阅读量: 38 作者: JC Morgan 摘要: There is no category base for which the σ-field of sets with the Baire property coincides with the σ-field of linear Borel sets. DOI: 10.1090/S0002-9939-1984-0727243-...
Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent....
Twitter Google Share on Facebook sigma algebra [′sig·mə ′al·jə·brə] (mathematics) A collection of subsets of a given set which contains the empty set and is closed under countable union and complementation of sets. Also known as sigma field. ...