On idempotent Liftings
On indecomposable sets with applications
In this note we show the characteristic function of every indecomposable set F in the plane is BVequivalent to the characteristic function a closed set See Formula in PDF See Formula in PDF . We show by example this is false in dimension three and above. As a corollary to this result we show that for everyϵ > 0 a set of finite perimeter Scan be approximated by a closed subset See Formula in PDF See Formula in PDF with finitely many indecomposable components and with the property that See...
On infinite composition of affine mappings
Let be affine mappings of . It is well known that if there exists j ≤ 1 such that for every the composition (1) is a contraction, then for any infinite sequence and any , the sequence (2) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any and any belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every the composition (1) is a contraction. This result...
On inhomogeneous self-similar measures and their spectra
Let for i = 1,..., N be contracting similarities, let be a probability vector and let ν be a probability measure on with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on such that . We give satisfactory estimates for the lower and upper bounds of the spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular, we...
On injective holomorphic Fredholm mappings of index 0 in complex Banach spaces
On Integral Representation and the Choquet Boundary for Convolution Algebras of Measures.
On integration and the Radon-Nikodym theorem in quasicomplete locally convex topological vector spaces.
On integration in Banach spaces, I
On integration in Banach spaces, III
On integration in Banach spaces, IV
On integration in Banach spaces, IX. Integration with respect to polymeasures
On integration in Banach spaces, V
On integration in Banach spaces, VI
On integration in Banach spaces, VII
On integration in Banach spaces, VIII. Polymeasures
On integration in Banach spaces. X: Integration with respect to polymeasures
On integration in Banach spaces, XI. Integration with respect to polymeasures
On integration in Banach spaces, XII. Integration with respect to polymeasures
On integration in Banach spaces, XIII. Integration with respect to polymeasures
On integration in compact metric spaces