Dimension zero vs measure zero

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Zero Measure

We study the almost Mathieu operator: 1) + cos(2n +)u(n), on l 2 (Z), and show that for all ; , and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely j4 ? 2jjj. In particular, for jj = 2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and jj = 2) we show that the Hausdorr dimension of the spectrum is smaller than or equal to 1=2.

متن کامل

Universal Measure Zero, Large Hausdorff Dimension, and Nearly Lipschitz Maps

We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric s...

متن کامل

Invariant Sets with Zero Measure and Full Hausdorff Dimension

For a subshift of finite type and a fixed Hölder continuous function, the zero measure invariant set of points where the Birkhoff averages do not exist is either empty or carries full Hausdorff dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages...

متن کامل

Closed Measure Zero Sets

We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1999

ISSN: 0002-9939,1088-6826

DOI: 10.1090/s0002-9939-99-05225-9