Displaying similar documents to “Exposed points in the set of representing measures for the disc algebra”

Representing measures for the disc algebra and for the ball algebra

Raymond Brummelhuis, Jan Wiegerinck (1991)

Annales Polonici Mathematici

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We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.

On a one-dimensional analogue of the Smale horseshoe

Ryszard Rudnicki (1991)

Annales Polonici Mathematici

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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.

A new proof of Kelley's Theorem

S. Ng (1991)

Fundamenta Mathematicae

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Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.