Dani, S. G.
(1992)
*Invariance groups and convergence of types of measures on lie groups*
Mathematical Proceedings of the Cambridge Philosophical Society, 112
(1).
pp. 91-108.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S030500410007078X

## Abstract

Let G be a connected Lie group and let {λ _{i}} be a sequence of probability measures on G converging (in the usual weak topology) to a probability measure λ . Suppose that {a_{i}} is a sequence of affine automorphisms of G such that the sequence {α _{i},(λ _{i})} also converges, say to a probability measure μ . What does this imply about the sequence {α _{i}}? It is a classical observation that if G = R^{n} for some n, and neither of λ and μ is supported on a proper affine subspace of R^{n}, then under the above condition, {α _{i}} is relatively compact in the group of all affine automorphisms of R^{n}.

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ID Code: | 8238 |

Deposited On: | 26 Oct 2010 12:06 |

Last Modified: | 30 May 2011 06:06 |

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