| Abstract |
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Haar measure and Hausdorff dimension are two possible methods of
measuring size in the field of \(p\)-adic numbers and its finite
extensions. We first explore the Haar measure and Hausdorff dimension
for balls in a finite extension of the \(p\)-adic number. Then we use
these two tools to measure the size of the Julia set for some
\(p\)-adic repellers. Finally, we give some concrete polynomial
examples from among these \(p\)-adic repellers.
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