Weak convergence of probability measures in the spaces of continuously differentiable functions. (English. Russian original) Zbl 0842.46026
Sib. Math. J. 34, No. 1, 123-127 (1993); translation from Sib. Mat. Zh. 34, No. 1, 140-144 (1993).
Summary: A criterion for weak convergence of probability measures in the spaces of continuously differentiable functions \(C^p(X)\), \(X\subset \mathbb{R}^k\), is proved. As a consequence spectral conditions of relative compactness for a sequence of homogeneous fields and a central limit theorem in \(C^p(X)\) are established.
MSC:
| 46G12 | Measures and integration on abstract linear spaces |
| 46E27 | Spaces of measures |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
| 60F05 | Central limit and other weak theorems |
Keywords:
weak convergence of probability measures; spaces of continuously differentiable functions; spectral conditions; relative compactness for a sequence of homogeneous fields; central limit theoremReferences:
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