Linear Operations on Summable Functions
نویسندگان
چکیده
منابع مشابه
Essential Supremum and Supremum of Summable Functions
Let D lR N , 0 < (D) < +1 and f : D ! lR is an arbitrary summable function. Then the function F() := R fx2D:f(x)g (f(x) ?) dd (2 lR) is continuous, non-negative, non-increasing, convex, and has almost everywhere the derivative F 0 () = ?f ]. Further on, it holds ess supf = supf 2 lR : F() > 0g, where ess supf denotes the essential supremum of f. These properties can be used for computing esssup...
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چکیده ندارد.
15 صفحه اولLinear Functions Preserving Sut-Majorization on RN
Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1940
ISSN: 0002-9947
DOI: 10.2307/1989960