کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591304 | 1335022 | 2010 | 58 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The disintegration of the Lebesgue measure on the faces of a convex function
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The disintegration of the Lebesgue measure on the faces of a convex function The disintegration of the Lebesgue measure on the faces of a convex function](/preview/png/4591304.png)
چکیده انگلیسی
We consider the disintegration of the Lebesgue measure on the graph of a convex function f:Rn→R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure on the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green–Gauss formula for these directions holds on special sets.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 258, Issue 11, 1 June 2010, Pages 3604-3661
Journal: Journal of Functional Analysis - Volume 258, Issue 11, 1 June 2010, Pages 3604-3661