Let X be a compact metric space, f a continuous transformation on X, and Y a vector space with linear compatible metric. Denote by M(X) the collection of all the probability measures on X. For a positive integer n, define the nth empirical measure L n : X → M(X) aswhere δ x denotes the Dirac measure at x. Suppose : M(X) → Y is continuous and affine with respect to the weak topology on M(X). We think of the compositeas a continuous and affine deformation of the empirical measure L n . The set of divergence points of such a deformation is defined as D(f, ) = {x ∈ X | the limit of L n x does not exist}.In this paper we show that for a continuous transformation satisfying the specification property, if (M(X)) is a singleton, then set of divergence points is empty, i.e. D(f, ) = ∅, and if (M(X)) is not a singleton, then the set of divergence points has full topological entropy, i.e. h top (D(f, )) = h top (f ).

and Key Results 0 The last two decades have witnessed an unprecedented transfer of Western management education theories and pedagogies into China and most Chinese MBA programs are now being modeled on their Western counterparts. 0 To gauge the impact of this infusion of Western methods and theories on China's management educational system, we have conducted a narrative analysis of Chinese MBA teaching cases published before and after this transfer. 0The holistic approach to management, prevalent in early Chinese MBA cases and typical of traditional Chinese culture, has largely disappeared and Chinese cases now exhibit many of the same weaknesses and deficiencies that have been documented in Harvard Business School cases.

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Link to this article: http://journals.cambridge.org/abstract_S0143385708000655 How to cite this article: DE-JUN FENG and LIN SHU (2009). Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages.Abstract. The paper is devoted to the study of the multifractal structure of disintegrations of Gibbs measures and conditional (random) Birkhoff averages. Our approach is based on the relativized thermodynamic formalism, convex analysis and, especially, the delicate constructions of Moran-like subsets of level sets.

Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes