Encyclopedia > Q > Quasi-invariant measure
Quasi-invariant measure
In mathematics, a quasi-invariant measure ÎĽ with respect to a transformation T, from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function by T. An important class of examples occurs when X is a smooth manifold M, T is a diffeomorphism of M, and ÎĽ is any measure that locally is a measure with base the Lebesgue measure on Euclidean space.
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