کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6426014 1345409 2012 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Set-valued functions, Lebesgue extensions and saturated probability spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Set-valued functions, Lebesgue extensions and saturated probability spaces
چکیده انگلیسی

Recent advances in the theory of distributions of set-valued functions have been shaped by counterexamples which hinge on the non-existence of measurable selections with requisite properties. These examples, all based on the Lebesgue interval, and initially circumvented by Sun in the context of Loeb spaces, have now led Keisler and Sun (KS) to establish a comprehensive theory of the distributions of set-valued functions on saturated probability spaces (introduced by Hoover and Keisler). In contrast, we show that a countably-generated extension of the Lebesgue interval suffices for an explicit resolution of these examples; and furthermore, that it does not contradict the KS necessity results. We draw the fuller implications of our theorems for integration of set-valued functions, for Lyapunov's result on the range of vector measures and for the theory of large non-anonymous games.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 229, Issue 2, 30 January 2012, Pages 1080-1103
نویسندگان
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