Cesàro Convergence via L² Bounds — Re-export Shim #
This file is the umbrella for Kallenberg's L² approach to Cesàro convergence of block averages of contractable sequences. Following the split for maintainability, the contents now live in four sub-files:
CesaroConvergence/KallenbergBound.lean—kallenberg_L2_bound(Kallenberg Lemma 1.2; retained for documentation but unused by the active proof)CesaroConvergence/Cauchy.lean—blockAvg_cauchy_in_L2,blockAvgFrozen(block averages are Cauchy in L²)CesaroConvergence/L2.lean—cesaro_to_condexp_L2,blockAvg_measurable_tailFamily(L² convergence to the tail conditional expectation)CesaroConvergence/L1.lean—cesaro_to_condexp_L1(L¹ form, consumed byAlphaConvergence.lean)
Existing call sites continue to work via this umbrella import.
References #
- Kallenberg (2005), Probabilistic Symmetries and Invariance Principles, Chapter 1, Lemma 1.2 and "Second proof"