条约
发表于 2025-3-27 00:58:01
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amphibian
发表于 2025-3-27 02:19:40
https://doi.org/10.1007/978-3-476-03535-6 specify probabilities .(.) for all . ∈ ℱ. Instead, we only gave the values of .(.) for events . in a smaller collection ε such that ℱ . σ(ε), and then we assumed without proof that . could be extended in a unique way to all of ℱ. In this chapter, we close this gap by showing that under certain natu
Neuralgia
发表于 2025-3-27 05:46:43
,Die Literatur Der Frühen Republik,the phrase “expectation of a random variable”, but instead we introduce the ‘integral’ of a measurable function. This new kind of integral is called the ‘Lebesgue integral’. Our second goal is to introduce several tools, which along with the Monotone Convergence Theorem, are valuable for interchangi
熔岩
发表于 2025-3-27 11:21:49
,Romantik und ›American Renaissance‹,giving the basic definitions, we prove the existence of ‘product measure’ and also give an important result concerning integration with respect to product measure (the Fubini Theorem). Important relations among expectations, independence, and densities are described. The last three sections of the c
confederacy
发表于 2025-3-27 14:52:31
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Concrete
发表于 2025-3-27 18:56:50
https://doi.org/10.1007/978-3-476-00421-5ically distributed random variables. Important in the study of random walks (and of more general random sequences) are ‘filtrations’ and ‘stopping times’. A filtration is a sequence of σ-fields representing the information available at various stages of an experiment. A stopping time is a ℤ̄. -value
天然热喷泉
发表于 2025-3-27 23:24:35
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眨眼
发表于 2025-3-28 05:46:43
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radiograph
发表于 2025-3-28 06:58:15
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Graphite
发表于 2025-3-28 11:48:05
Wirtschaftspolitische Grundlagen partial sum of a series of independent random variables. Our first result is that convergence in distribution of (..) is equivalent to a.s. convergence. Thereafter, we specialize to the case in which (.., ..,...) is an iid sequence. Further limit theorems involving more general sums of independent