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Register a new userLaw of the Large Numbers for Random Functions with two Variables
قانون الأعداد الكبيرة للدوال العشوائية بمتحولين
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نقوم في هذا البحث بإيجاد قانون الأعداد الكبيرة للدوال العشوائية المحدبة – المقعرة المغلقة و نعمِّم بعض النتائج المتعلقة بالدوال نصف المستمرة من الأدنى ذات المتحول الواحد إلى نتائج مشابهة تخص دوال محدبة – مقعرة بمتحولين و ذلك باستخدام الدوال القرينة المحدبة لدالة محدبة – مقعرة و تقارب موسكو فوق /تحت البياني.
In this research we will find a law of the large numbers for random convex – concave closed functions, and generalize some results related to lower semi- continuous functions to similar results concerning the convex– concave functions, and that will be done with using the parent convex functions and the Mosco-epi \ hypo-convergence.
References used
ARTSTEIN,Z. ; HART,S. : Law of large numbers for random sets and allocation processes, Mathematics of Operations Research 6 (1981), 482-492
ARTSTEIN,Z.; VITALE,R.A. : A strong law of large numbers for random compact sets, The Annals of Probability, vol. 3, no. 5(1975), 879–882
ATTOUCH, H. : Variational convergence for functions and operators, Pitman, London, 1984, 420
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