We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorial optimization. We show how invariance of hyperfiniteness of graphings under local isomorphism can be reformulated as an infinite version of a natural combinatorial optimization problem, and how one can prove it by extending wellknown proof techniques (linear relaxation, greedy algorithm, linear programming duality) from the finite case to the infinite.

中文翻译：

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超有限图形和组合优化

我们展示了在度量保留映射下推进可测量集的问题与组合优化中的线性松弛之间的类比。我们展示了如何将局部同构下图形的超有限性不变性重新表述为自然组合优化问题的无限版本，以及如何通过扩展众所周知的证明技术（线性松弛、贪婪算法、线性规划对偶性）从有限情况到无限。