This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed ...This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.展开更多
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ if and only if L( *υ)...In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ if and only if L( *υ)L( *μ) and d(L( *υ))/d(L( *μ))= 0( *(dμ/dυ)) . We shall define the Loeb space of σ finite measure space by a natural way and prove that the results above can be extended to σ finite measure spaces.展开更多
For any irreducible complex projective variety A,we prove that in the nonstandard ex-tension ~*A of A in a polysaturated model,the set of points which are not generic points of A has Loebmeasure zero.This is similar t...For any irreducible complex projective variety A,we prove that in the nonstandard ex-tension ~*A of A in a polysaturated model,the set of points which are not generic points of A has Loebmeasure zero.This is similar to the Sard theorem asserting that the critical values of a smooth maphave Lebesgue measure zero.展开更多
In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on...In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.展开更多
It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb...It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).展开更多
This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated non...This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated nonstandard extension of x.A nonstandsrd exchange economy model is established on a commeodity space ^*E.where E∈x is a standard normed Riesz space.in this model the set of consumers is a hyperfinite(really infinite)st,denoted by T={1,2，…，ω}，（ω∈^*N-N),and the preference of each consumer t is an internal binary relation,>t on his consumption set Xt such that x ≯x for any x∈Xt,Each consumption set Xi is assumed to satisfy that(1),int E+Xt∩ E+≠φ，and (2),y >x implies y ∈ Xt for any x ∈nx Xt and y∈ ns ^*E.It is that if the preferences are monotonic for almost all consumers,then the core of the economy coincides with the set of all competitive equilibria.It is also showed that when the set of comsumers who have monotonic preferences is nonnegligible,an allocation is an core allocation if and only if it issupported by prices,and if and only if it is strongly supported by prices.展开更多
博士后岗位[美国]Johns Hopkins University A funded postdoctoral position is available in the research laboratoryof Dr.David Loeb in the Department of Oncology of Johns Hopkins University. The laboratory has basic and t...博士后岗位[美国]Johns Hopkins University A funded postdoctoral position is available in the research laboratoryof Dr.David Loeb in the Department of Oncology of Johns Hopkins University. The laboratory has basic and translational projects insarcoma biology and tumor angiogenesis,展开更多
基金Supported by the Natural Science Foundation of Shaanxi Province(2007A12)
文摘This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
文摘In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ if and only if L( *υ)L( *μ) and d(L( *υ))/d(L( *μ))= 0( *(dμ/dυ)) . We shall define the Loeb space of σ finite measure space by a natural way and prove that the results above can be extended to σ finite measure spaces.
文摘For any irreducible complex projective variety A,we prove that in the nonstandard ex-tension ~*A of A in a polysaturated model,the set of points which are not generic points of A has Loebmeasure zero.This is similar to the Sard theorem asserting that the critical values of a smooth maphave Lebesgue measure zero.
文摘In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.
基金The first author was partially supported by NSF grants DMS-0900938 and DMS-1162309The second author was partially supported by NSF grant DMS-1001625.
文摘We undertake a local analysis of combinatorial independence as it connects to topological entropy within the framework of actions of sofic groups.
基金Supported by the Special Science Foundation of the Education Committee of Shaanxi Province(03jk066)
文摘It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).
文摘This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated nonstandard extension of x.A nonstandsrd exchange economy model is established on a commeodity space ^*E.where E∈x is a standard normed Riesz space.in this model the set of consumers is a hyperfinite(really infinite)st,denoted by T={1,2，…，ω}，（ω∈^*N-N),and the preference of each consumer t is an internal binary relation,>t on his consumption set Xt such that x ≯x for any x∈Xt,Each consumption set Xi is assumed to satisfy that(1),int E+Xt∩ E+≠φ，and (2),y >x implies y ∈ Xt for any x ∈nx Xt and y∈ ns ^*E.It is that if the preferences are monotonic for almost all consumers,then the core of the economy coincides with the set of all competitive equilibria.It is also showed that when the set of comsumers who have monotonic preferences is nonnegligible,an allocation is an core allocation if and only if it issupported by prices,and if and only if it is strongly supported by prices.
文摘博士后岗位[美国]Johns Hopkins University A funded postdoctoral position is available in the research laboratoryof Dr.David Loeb in the Department of Oncology of Johns Hopkins University. The laboratory has basic and translational projects insarcoma biology and tumor angiogenesis,
