Displaying similar documents to “Uniform distribution preserving mappings”

Change of variables formula under minimal assumptions

Piotr Hajłasz (1993)

Colloquium Mathematicae

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In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We...

A central limit theorem for processes generated by a family of transformations

Marian Jabłoński

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Let τ n , n ≥ 0 be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let f n , n ≥ 0 be a sequence of elements of L 2 ( Ω , Σ , P ) with E f n = 0 . It is shown that the distribution of ( ∑ i = 0 n f i ∘ τ i ∘ . . . ∘ τ 0 ) ( D ( ∑ i = 0 n f i ∘ τ i ∘ . . . ∘ τ 0 ) ) - 1 tends to the normal distribution N(0,1) as n → ∞. 1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.