feat: prove Bochner's theorem via Gaussian smoothing#1
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Structure the proof of Bochner's theorem (continuous PD function with φ(0)=1 is a characteristic function) using Gaussian smoothing and Prokhorov's theorem. The main theorem is fully proved from two sorry'd helper lemmas: - exists_probMeasure_of_pd_integrable (Fourier inversion for PD L¹) - isTight_of_charFun_pointwise_tendsto (generalized tightness) Also adds norm_le_one for PD functions in PositiveDefinite.lean.
Keep Unit B's proved Schur product and strengthened definition, retain Unit D's norm_le_one (still sorry'd) in sorry audit.
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Summary
bochnertheorem inBochner.leanfrom two well-isolated sorry'd helpersintegrable_charFun_gaussianVar(Gaussian charfun integrability)norm_le_onefor positive definite functions inPositiveDefinite.leanSorry audit (Bochner.lean)
exists_probMeasure_of_pd_integrable— PD + L¹ + normalized implies characteristic function (requires Parseval)isTight_of_charFun_pointwise_tendsto— generalized tightness from charfun convergence to continuous limitTest plan
lake buildsucceeds