测度论研究的是测度空间，其中测度定义在一个 sigma-algebra 之上，但是我们有时候不一定能一下子得到整个 sigma-algebra 我们的想法是从一些集合构成的集类出发，再通过某些运算生成一个 sigma-algebra . Dynkin system 是从一种很容易满足的集类——我们称之为 pi system，仅仅满足对交集运算封闭——...
这个结论其实就是Dynkin定理,注意到”有限交封闭“,说的其实就是 \pi -system。我们可以对Dynkin定理进行如下表述: (1) \mathcal{P} 是一个 \pi -system, \mathcal{L} 是一个 \lambda -system,并且有 \mathcal{P}\subseteq \mathcal{L} ,那么有 \sigma(\mathcal{P})\subseteq \mathcal{L} 这个...
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pre-Dynkin systemDynkin systemcoherenceextendabilityquantum probabilityintersectionalityprevisionimprecise probabilitypartial expectationIn the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of ...
3 below [see (3.8)] to derive existence and uniqueness of the system of doubly reflected BSDEs which approximates the value process of the time-inconsistent zero-sum Dynkin game. The integrability condition in Assumption 2.1(i)–(c) can be removed at the cost of some additional technical ...
LetΦ be a root system with Dynkin diagram D. ThenΦ = Φ1 ⊕Φ2if and only if D can be decomposed as the union of two components D1and D2that are not connected and such that Di is the Dynkin diagram ofΦi for i = 1,2. Proof. First suppose that Φ = Φ1 ⊕Φ2. Let Δ...
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formalizes the proof of Dynkin's lemma in measure theory. Dynkin's lemma is a useful tool in measure theory and probability theory: it helps frequently to generalize a statement about all elements of a intersection-stable set system to all elements of the sigma-field generated by that system....
Twitter Google Share on Facebook root system (redirected fromAffine Dynkin diagram) Dictionary Thesaurus root system the total below-ground vegetative system of vascular plants. seeROOT. Collins Dictionary of Biology, 3rd ed. © W. G. Hale, V. A. Saunders, J. P. Margham 2005 ...
Dynkin’s lemma is a useful tool in measure theory and probability theory:it helps frequently to generalize a statement about all elements of a intersection-stable set system to all elements of the sigma-field generated by that system.MML Identifier:DYNKIN.WWW:http://mizar.org/JFM/Vol12/...