Measure Theoretic Laws for Lim Sup Sets is popular PDF and ePub book, written by Victor Beresnevich in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Measure Theoretic Laws for Lim Sup Sets can be Read Online from any device for your convenience.
Measure Theoretic Laws for Lim Sup Sets Book PDF Summary
Given a compact metric space $(\Omega, d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of '$\p$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities
Detail Book of Measure Theoretic Laws for Lim Sup Sets PDF
- Author : Victor Beresnevich
- Release : 19 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 1470404478
- Genre : Mathematics
- Total Page : 91 pages
- Language : English
- PDF File Size : 12,5 Mb
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