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Let G be a Lie group, H ≤ G a closed subgroup and M ≈ G/H. In [14] André Weil gave a necessary and sufficient condition for the existence of invariant measures on homogeneous spaces of arbitrary locally compact groups. For Lie groups using the structure theory we give a neater necessary and sufficient condition for the existence of a G-invariant measure on M, cf. Theorems (2.1) and (3.2) in the introduction. 相似文献
3.
Wolfgang Adamski 《Israel Journal of Mathematics》1989,65(1):79-95
Let (X,A) be a measureable space andT:X →X a measurable mapping. Consider a family ℳ of probability measures onA which satisfies certain closure conditions. IfA
0⊂A is a convergence class for ℳ such that, for everyA ∈A
0, the sequence ((1/n) Σ
i
=0/n−1
1
A
∘T
i) converges in distribution (with respect to some probability measurev ∈ ℳ), then there exists aT-invariant element in ℳ. In particular, for the special case of a topological spaceX and a continuous mappingT, sufficient conditions for the existence ofT-invariant Borel probability measures with additional regularity properties are obtained. 相似文献
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M. G. Nadkarni 《Proceedings Mathematical Sciences》1990,100(3):203-220
A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability
measure. 相似文献
5.
Several necessary and sufficient conditions are given for the existence of aσ-finite invariant measure for a positive operator onL
∞. They are ofσ-type: the entire space is an increasing union of setsX
k each of which is well-behaved.
To the Memory of Shlomo Horowitz
Research in part supported by the National Science Foundation (U.S.A.). 相似文献
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Javier Solano 《Bulletin of the Brazilian Mathematical Society》2013,44(1):67-103
We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicityalongtheleavesimpliesexistenceofafinitenumberofergodicabsolutely continuous invariant probability measures which describe the asymptotics of almost every point. The main technical tool is an extension for sequences of maps of a result of de Melo and van Strien relating hyperbolicity to recurrence properties of orbits. As a consequence of our main result, we also obtain a partial extension of Keller’s theorem guaranteeing the existence of absolutely continuous invariant measures for non-uniformly hyperbolic one dimensional maps. 相似文献
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Piotr Zakrzewski 《Israel Journal of Mathematics》1993,83(3):343-352
SupposeG is a group of measurable transformations of aσ-finite measure space (X,A, m). A setA ∈A is weakly wandering underG if there are elementsg
n ∈G such that the setsg
nA, n=0, 1,…, are pairwise disjoint. We prove that the non-existence of any set of positive measure which is weakly wandering
underG is a necessary and sufficient condition for the existence of aG-invariant, probability measure defined onA and dominating the measurem in the sense of absolute continuity.
This paper was written while the author was visiting the Technische Universitat Berlin as a research fellow of the Alexander
von Humboldt Foundation. 相似文献
13.
Alberto Tonolo 《代数通讯》2013,41(2):437-455
A duality is introduced to prove the existance of a finest linear topology equivalent to a given one for linearly topologized modules. Various properties of this finest topology are obtained. 相似文献
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R. v. Vintschger 《Probability Theory and Related Fields》1989,82(2):307-313
Summary We prove the existence of an invariant measure for processes arising from a perturbation of theC[0,1]-valued Ornstein-Uhlenbeck process with a drift taking values in the Cameron-Martin space. We study the infinitesimal generator, and a partial integration onC[0,1] will yield conditions on the drift which enable us to use arguments of perturbation theory to prove the existence of an invariant measure which is absolutely continuous with respect to the Wiener measure. 相似文献
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In this paper, we prove that the existence of product stochastic measures depends on the axiom-system of set theory: If one accepts the axiom of choice, the answer is negative, and we give a counter-example where the product stochastic measure doesn't exist; but in the Solovay model (one kind of set theory which refuses the axiom of choice), the answer is positive, and we give a proof. 相似文献
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Wolfgang Adamski 《Rendiconti del Circolo Matematico di Palermo》1990,39(3):436-445
LetP be a Markov kernel defined on a measurable space (X,A). A probability measure μ onA is said to beP-invariant if μ(A=∫P(x,A)dμ(x) for allA ∈A∈A. In this note we prove a criterion for the existence ofP-invariant probabilities which is, in particular, a substantial generalization of a classical theorem due to Oxtoby and Ulam ([5]). As another consequence of our main result, it is shown that every pseudocompact topological space admits aP-invariant Baire probability measure for any Feller kernelP. 相似文献
17.
Let r 1, …, r m be positive real numbers and A 1, …, A m be n × n matrices with complex entries. In this article, we present a necessary and sufficient condition for the existence of a unitarily invariant norm ‖·‖, such that ‖A i ‖ = r i , for i = 1, …, m. Then we identify the greatest unitarily invariant norm which satisfies this condition. Using this, we get an approximation of unitarily invariant norms. Although the minimum unitarily invariant norm which satisfies this condition does not exist in general, we find conditions over A i s and r i s which are sufficient for the existence of such a norm. Finally, we get a characterization of unitarily invariant norms. 相似文献
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Sergey V. Astashkin Guillermo P. Curbera Konstantin E. Tikhomirov 《Mathematische Nachrichten》2016,289(2-3):175-186
We characterize rearrangement invariant spaces X on [0, 1] with the property that each orthonormal system in X which is uniformly bounded in some Marcinkiewicz space , for equivalent to , , is a system of Random Unconditional Convergence (RUC system). 相似文献
19.
Let X be a Polish space and P a Markov operator acting on the space of Borel measures on X. We will prove the existence of an invariant measure with respect to P, provided that P satisfies some condition of a Prokhorov type and that the family of functions is equi-continuous with respect to the Prokhorov distance at some point of the space X. Moreover, we will construct a counterexample which show that the above equi-continuity condition cannot be dropped. 相似文献