Contributed to the leanprover-community/mathlib4 repository by developing three advanced features over two months, focusing on formal verification and measure theory using Lean. Delivered a core lemma, IntegrableAtFilter.congr'_enorm, to streamline integrability proofs via filter equality of extended norms, enhancing proof flexibility and reuse within the Carleson project. Added the norm_I theorem for RCLike, handling conditional cases with Lean’s grind tactic, and introduced new lemmas relating essential supremum to indexed supremum to support measure-theoretic arguments. Emphasized code maintainability and upstream integration, demonstrating depth in mathematics, formal verification, and Lean, while improving proof automation and library robustness.