پديد آورنده :
باغبان، مهدي محمد
عنوان :
بررسي فضاهاي نرمدار و ضرب داخلي احتمالي
گرايش تحصيلي :
آناليز تابعي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
فريد بهراني
استاد مشاور :
محمدرضا كوشش
تاريخ نمايه سازي :
25/1/93
استاد داور :
محمود لشگري زاده، كوروش نوروزي، رسول نصر اصفهاني
كد ايرانداك :
ID601 دكتري
چكيده انگليسي :
Study of Probabilistic Normed and Inner Product spaces Mehdi Mohammadbaghban baghban@math iut ac ir December 11 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Farid Bahrami fbahrami@cc iut ac ir Advisor Mohammad Reza Koushesh koushesh@cc iut ac ir Isfahan University of Technology Isfahan 84156 83111 IranAbstractIn this thesis we introduce the notion of probabilistic valued measures as a generaliza tion of non negative measures and construct the corresponding Lp spaces for distribu tions p 0 It is also shown that if the distribution p satis es p 1 then as in theclassical case these spaces are complete probabilistic normed spaces Keywords probabilistic normed space probabilistic valued measure probabilistic Lp spaces MSC 2010 Primary 60A10 Secondary 46B0 1 IntroductionThe idea of Probabilistic Normed spaces brie y PN spaces was introduced by erstnevin 1963 in 9 and 8 who replaced R the set of all non negative real numbers withthe elements of certain subset of extended distribution functions as the targetspace of the norm function These spaces and their related notions were then studiedby many authors among which we may refer to 1 3 5 7 10 and the text 6 There is also a generalization of this notion introduced in 2 However in this paperwe consider probabilistic normed spaces still in the sence of erstnev Using his idea we introduce here the notion of probabilistic valued measures and corresponding Lpspaces for a distribution function p The title of the paper arises om the fact that notonly the measure and the exponent p have probabilistic natures but also the elementsof the spaces Lp introduced in the last section are functions with values in a certainprobabilistic normed space We rst recall some de nitions and notations Let bethe set of all extended distribution functions i e the set of all non decreasing andle continuous functions F R 0 1 and let D be the set of all F withinf F R 0 and sup F R 1 The set can be embedded in by the map r r where r r forr R and R and Here A denotes the characteristic function of aset A There is a metric on known as Levy metric which for every F G is de ned as
استاد راهنما :
فريد بهراني
استاد مشاور :
محمدرضا كوشش
استاد داور :
محمود لشگري زاده، كوروش نوروزي، رسول نصر اصفهاني
