منابع مشابه
The Lebesgue Monotone Convergence Theorem
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The monotone convergence theorem holds for the Riemann integral, provided (of course) it is assumed that the limit function is Riemann integrable. It might be thought, though, that this would be difficult to prove and inappropriate for an undergraduate course. In fact the identity is elementary: in the Lebesgue theory it is only the integrability of the limit function that is deep. This article...
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The decomposition theorem named after Lebesgue asserts that certain set functions have canonical representations as sums of particular set functions called the absolutely continuous and the singular ones with respect to some fixed set function. The traditional versions are for the bounded measures with respect to some fixed measure on a σ algebra, in final form due to Hahn 1921, and for the bou...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2008
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-008-0023-1