How Long to Read Measure Theoretic Laws for lim sup Sets

How Long Does it Take to Read Measure Theoretic Laws for lim sup Sets?

It takes the average reader 1 hour and 58 minutes to read Measure Theoretic Laws for lim sup Sets by Victor Beresnevich Detta Dickinson Sanju Velani

Assuming a reading speed of 250 words per minute. Learn more

Description

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 `$\psi$-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. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.

How long is Measure Theoretic Laws for lim sup Sets?

Measure Theoretic Laws for lim sup Sets by Victor Beresnevich Detta Dickinson Sanju Velani is 116 pages long, and a total of 29,696 words.

This makes it 39% the length of the average book. It also has 36% more words than the average book.

How Long Does it Take to Read Measure Theoretic Laws for lim sup Sets Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 42 minutes to read Measure Theoretic Laws for lim sup Sets aloud.

What Reading Level is Measure Theoretic Laws for lim sup Sets?

Measure Theoretic Laws for lim sup Sets is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Measure Theoretic Laws for lim sup Sets?

Measure Theoretic Laws for lim sup Sets by Victor Beresnevich Detta Dickinson Sanju Velani is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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