We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is characterized in terms of distributions on iterated degree measures, Markov operators, weak isomorphism of a conditional expectation with respect to invariant sub-σ-algebras and isomorphism of certain quotients of given graphons.

中文翻译：

---

石墨子的分数同构

我们将石墨子的分数同构理论作为对有限图分数同构的经典理论的推广。泛化是根据有限树的同态密度给出的，它的特征是迭代度测量的分布、马尔可夫算子、条件期望关于不变子σ -代数的弱同构和给定的某些商的同构石墨烯。