Algebraic structures generated by almost continuous functions
En este trabajo se propone una estructura de álgebra difusa (borrosa) basada en la distinción entre difusidad extensiva y comprehensiva, desarrollando y conectando los trabajos de Nahmias sobre variables difusas, de Klement sobre medibilidad difusa y de Nowakowska sobre estructuras de conceptos.
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Let be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of is Borel isomorphic to an almost 1-1 extension of . Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz...
Let (X, μ) be a σ-finite measure space and let τ be an ergodic invertible measure preserving transformation. We study the a.e. convergence of the Cesàro-α ergodic averages associated with τ and the boundedness of the corresponding maximal operator in the setting of Lp,q(wdμ) spaces.
It is well-known that a probability measure on the circle satisfies for every , every (some) , if and only if for every non-zero ( is strictly aperiodic). In this paper we study the a.e. convergence of for every whenever . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of , for the strong sweeping out property (existence of a Borel set with a.e. and a.e.). The results are extended to general compact Abelian groups with Haar...
Bellow and Calderón proved that the sequence of convolution powers converges a.e, when is a strictly aperiodic probability measure on such that the expectation is zero, , and the second moment is finite, . In this paper we extend this result to cases where .
Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series converges almost everywhere with respect to Lebesgue measure provided that .
We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.
We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.