Displaying similar documents to “On the uniqueness property for products of symmetric invariant probability measures.”

On a one-dimensional analogue of the Smale horseshoe

Ryszard Rudnicki (1991)

Annales Polonici Mathematici


We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have φ ( T n x ) f ( x ) d x φ d μ , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then n - 1 i = 0 n - 1 φ ( T i x ) φ d μ for Lebesgue-a.e. x.