Entropy Regular Sets
نویسندگان
چکیده
One of the objects of geometric measure theory is to derive global geometric structures from local properties (densities with respect to the s{dimensional Hausdorr measure). In the framework of dynamical system it is more natural to consider entropy measures instead of Hausdorr measures. Our aim is to show that regular subshifts (with respect to the entropy measure) necessarily have a special rigid structure. Moreover, their entropy has to be the logarithm of an integer. This parallels the well known fact that regular sets (with respect to the Hausdorr measure) have to have integral dimension.
منابع مشابه
THE ENTROPIES OF THE SEQUENCES OF FUZZY SETS AND THE APPLICATIONS OF ENTROPY TO CARDIOGRAPHY
In this paper, rstly we have introduced to entropy of sequences of fuzzy sets and given sometheorems about it. Secondly, the waves P and T which appears in electrocardiograms weretransferred to fuzzy sets, by using denition of entropy for sequences of fuzzy sets, and somenumerical values were obtained for sequences of waves P and T. Thus any person can makea medical predictions for some cardiac...
متن کاملRegular Language Distance and Entropy
This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular language plays a large role in the extension. Much of the paper is spent investigating the entropy of a regular language. This includes addressing issues that have ...
متن کامل$r$-fuzzy regular semi open sets in smooth topological spaces
In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...
متن کاملA Framework for Optimal Attribute Evaluation and Selection in Hesitant Fuzzy Environment Based on Enhanced Ordered Weighted Entropy Approach for Medical Dataset
Background: In this paper, a generic hesitant fuzzy set (HFS) model for clustering various ECG beats according to weights of attributes is proposed. A comprehensive review of the electrocardiogram signal classification and segmentation methodologies indicates that algorithms which are able to effectively handle the nonstationary and uncertainty of the signals should be used for ECG analysis. Ex...
متن کاملBowen Lemma in the Countable Symbolic Space
We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent of the Gibbs measure, are given by a variational principle, which generalizes Li and Ma’s result and Bowen’s result.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999