منابع مشابه
Applications of Cohomology to Set Theory I: Hausdorff Gaps
We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. This leads to a natural equivalence notion for gaps about which we answer questions by constructing many simultaneous gaps. The first result is proved in ZFC while new combinatorial hypotheses generalizing 4 are introduced to prove the second result. The cohomology the...
متن کاملHausdorff measure
Here, instead of taking a σ-algebra as given and then defining a measure on this σ-algebra (namely, on the measurable sets), we take an outer measure as given and then define measurable sets using this outer measure. Carathéodory’s theorem states that the collection M of ν-measurable sets is a σ-algebra and that the restriction of ν to M is a complete measure. Suppose that (X, ρ) is a metric sp...
متن کاملHistoric set carries full hausdorff dimension
We prove that the historic set for ratio of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional non-uniformly hyperbolic dynamical systems.
متن کاملEffective Hausdorff Dimension
We continue the study of effective Hausdorff dimension as it was initiated by LUTZ. Whereas he uses a generalization of martingales on the Cantor space to introduce this notion we give a characterization in terms of effective s-dimensional Hausdorff measures, similar to the effectivization of Lebesgue measure by MARTIN-LÖF. It turns out that effective Hausdorff dimension allows to classify sequ...
متن کاملEffective Hausdorff dimension
Lutz (2000) has recently proved a new characterization of Hausdorff dimension in terms of gales, which are betting strategies that generalize martingales. We present here this characterization and give three instances of how it can be used to define effective versions of Hausdorff dimension in the contexts of constructible, finite-state, and resource-bounded computation.
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ژورنال
عنوان ژورنال: Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi
سال: 2019
ISSN: 2146-538X
DOI: 10.17714/gumusfenbil.548506