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The main purpose of the article under review is to relate topological and ergodic properties of algebraically defined transformations on compact subsets of the field of all rational \(p\)-adic numbers \(\mathbb{Q}_p\). The authors start from basic simple notions and develop the relevant topological and measure theoretic concepts in a highly illuminating way. At first they give an introduction to \(p\)-adic numbers. Then they introduce the concept of minimality of a continuous transformation \(T:X \to X\) on a topological space \(X\) which means that each orbit \(\partial(x) :=\{T^n(x)\}_{n=-\infty}^\infty\) is dense in \(X\). In order to define the necessary concepts from ergodic theory the authors build up a measure which turns out to be the Haar measure on the locally compact group \(\mathbb{Q}_p\); this measure, applied to a ball in \(\mathbb{Q}_p\), is the radius of this ball. The main results are proved in full detail and should be accessible to everyone with a mathematical education in basic analysis, algebra and number theory.