A special class of doubly stochastic (Markov) operators is constructed. In a sense these operators come from measure preserving transformations and inherit some of their properties, namely ergodicity and positivity of entropy, yet they may have no pointwise factors.

中文翻译：

---

爆炸式马尔可夫算子

构造一类特殊的双随机（Markov）算子。从某种意义上说，这些算子来自保持度量的变换，并继承了它们的某些属性，即遍历性和熵的正性，但它们可能没有指向性因素。