Irremediable 发表于 2025-3-28 15:17:42
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http://reply.papertrans.cn/32/3157/315658/315658_42.pngAmplify 发表于 2025-3-29 01:47:49
https://doi.org/10.1007/978-3-642-86007-2on on the power set .. (3) Finally, we show that this outer measure . induces a .-algebra . of subsets of . (such that .) upon which the restriction . is a measure on the .-algebra .. This is the Carathéodory Extension Theorem, which is the central result of this chapter, whose applications go as far as Chapters ., ., and ..Ganglion 发表于 2025-3-29 05:54:40
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Remarks on Integralsn we summarize the basic properties of integrals with respect to a positive measure, as discussed in Chapters 3, 4, and 5. These basic properties will be extended to integrals with respect a signed measure and with respect to a complex measure in the forthcoming sections.Semblance 发表于 2025-3-29 19:02:33
xt is self-contained and requires only modest prerequisites.Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, whereMANIA 发表于 2025-3-29 23:22:02
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