دانلود مقاله ISI انگلیسی شماره 8672
عنوان فارسی مقاله

قرارگیری تداوم مجموعه کراندار برای بردار غیر قابل اندازه گیری، توپولوژی و کاربردهای آن برای نظریه تعادل اقتصادی

کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات
8672 2000 9 صفحه PDF سفارش دهید محاسبه نشده
خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.
عنوان انگلیسی
Localisation of continuity to bounded sets for nonmetrisable vector topologies and its applications to economic equilibrium theory
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Indagationes Mathematicae, Volume 11, Issue 1, 2000, Pages 53–61

کلمات کلیدی
- تداوم - مجموعه کراندار - بردار غیر قابل اندازه گیری - توپولوژی - نظریه تعادل اقتصادی
پیش نمایش مقاله
پیش نمایش مقاله قرارگیری تداوم مجموعه کراندار برای بردار غیر قابل اندازه گیری، توپولوژی و کاربردهای آن برای نظریه تعادل اقتصادی

چکیده انگلیسی

We present two ‘localisation’ techniques which facilitate verifications of the topological properties of sets, functions and correspondences needed in, e.g., economic equilibrium analysis with infinite-dimensional commodity spaces. The first uses the Krein-Smulian theorem, which shows that weak∗ upper semicontinuity of a concave function on a dual Banach space is equivalent to bounded weak∗ u.s. continuity. The second is based on the continuity of lattice operations: for a nondecreasing function on a topological vector lattice, we show that lower semicontinuity on a set bounded from below is equivalent to l.s. continuity on bounded subsets. In the case of L∞, we use convergence in measure to establish thatsequential semicontinuity, lower for the Mackey topology or upper for the weak∗ one, is equivalent to semicontinuity. This greatly simplifies some arguments; e.g., the Mackey continuity of a concave, nondecreasing integral functional on L+∞ becomes an immediate consequence of Lebesgue's Dominated Convergence Theorem. Other uses in mathematical economics are also discussed.

مقدمه انگلیسی

We present two localisation’ techniques which facilitate verifications of the topological properties of sets, functions and correspondences needed in, e.g., economic equilibrium analysis with infinite dimensional commodity spaces. The first uses the Krein-Smulian theorem,which shows that weak* upper semicontinuity of a concave function on a dual Banach space is equivalent to bounded weak* U.S. continuity. The second is based on the continuity of lattice operations: for a nondecreasing functionon a topological vector lattice, we show that lower semicontinuity on a set bounded from below is equivalent to1,s. continuity on bounded subsets. In the case of L”, we use convergence in measure to establish that sequential semicontinuity, lower for the Mackey topology or upper for the weak*one, is equivalent to semicontinuity. This greatly simplifiessome arguments; e.g., the Mackey continuity of a concave, nondecreasing integral functional on L+”becomes an immediate consequence of Lebesgue’s Dominated Convergence Theorem. Other uses in mathematical economics are also discussed.

خرید مقاله
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