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For the Gibbs measure which is obtained as the limit of finite size Gibbs measures with free boundary con- dition, a central limit theorem is also proved, but the limit is not
The symplectic convexity theorem states that the image under the moment map of a compact connected symplectic manifold with Hamiltonian torus action is a convex polytope..
After that we give the proof of the main theorem which is based on Theorem 2.1 to be proved below and our results obtained previously [7] (see also [8]) for fractional integrals
The following theorems, proved in [2], therefore hold, the first showing that the neutrix convolution product is a generaliza- tion of the convolution product..
(2) Theorem 7(b) for Banach spaces and Γ = X ′ is proved in [9]; the case of complete separable metrizable topological vector spaces and arbitrary Γ is considered in [10] (see also
The notion of leaf-to-leaf transforming homotopic mappings is introduced, and the homotopy axiom for vertical cohomologies is proved (Theorem 2.5).. The notion of a relative group
It is proved that any small dissipation inside the domain is sufficient to uniformly stabilize the solution of this equation by means of a nonlinear feed- back of memory type acting
The following fixed point theorem for the nonlinear contraction is well-known and useful for proving the existence and the uniqueness theorems for the nonlinear differ- ential
