منابع مشابه
The Vitali covering theorem in constructive mathematics
This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vitali Cover one can find a finite family of pairwise disjoint sets in the Vitali Cover that cover the entire ...
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In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...
متن کاملVitali Convergence Theorem for Upper Integrals
It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...
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The standard techniques used to prove the Lebesgue differentiation theorem (that monotonic functions are a.e. differentiable) are presented in an unusual way that reveals more about their nature and allows greater generality.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1975
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-34-1-69-72