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I guess Mach's Principle went into Einstein's thought on Cosmological Models. In fact, probably the main reason he introduced the Cosmological Constant was to get a finite universe to keep any particle not infinity apart from the rest of the mass of the universe because General Relativity allow for other solutions. Inertia is determined by the metric structure of the space-time. Sure it is related to the universe mass by Einstein equations, but once you solve it and have the metric, the inertia of any particle depends only on local properties of the geometry. I think that is Wheeler's great insight on this subject.