Approaches to Quantum Gravity

The causal set approach to Quantum Gravity 423approximation exists. Nonetheless, you might imagine extending the definitionof the continuum approximation to some fractals, by carrying outsprinklings of these structures, and then ask how the new dimension estimatorscompare to the more standard estimators of Hausdorff and Lebesque.It seems plausible that the causal set estimators we have would be moresimilar to the measure theoretic dimensions like the Hausdorff or Minkowski–Bouligand dimension (since the Lebesque measure is, I think, invariant underhomeomorphisms, which seems at odds with scale-dependent dimension estimators),but this is not known (a question that is under investigation by DavidMeyer).