OAI/Probability/GaussianReplacement/Gram.lean

GitHub source file

28 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.CurrentProjection.gram_linear_combination line 15
  2. def OAI.CurrentProjection.gsUpper line 29
  3. lemma OAI.CurrentProjection.gsUpper_expansion line 33
  4. lemma OAI.CurrentProjection.gsUpper_det line 44
  5. lemma OAI.CurrentProjection.gram_gramSchmidt_diagonal line 52
  6. theorem OAI.CurrentProjection.det_gram_eq_prod_gramSchmidt line 63
  7. lemma OAI.CurrentProjection.sub_gramSchmidt_mem_span line 77
  8. lemma OAI.CurrentProjection.gramSchmidt_mem_span_orthogonal line 86
  9. lemma OAI.CurrentProjection.gramSchmidt_eq_sub_starProjection line 98
  10. lemma OAI.CurrentProjection.norm_gramSchmidt_eq_infDist line 106
  11. lemma OAI.CurrentProjection.infDist_affine_mk' line 113
  12. lemma OAI.CurrentProjection.norm_gramSchmidt_sub_eq_affine_infDist line 127
  13. lemma OAI.CurrentProjection.image_Iio_castSucc line 134
  14. lemma OAI.CurrentProjection.image_Iio_last line 145
  15. lemma OAI.CurrentProjection.gramSchmidt_castSucc line 154
  16. lemma OAI.CurrentProjection.measurable_gramSchmidt line 160
  17. lemma OAI.CurrentProjection.lintegral_pi_snoc line 182
  18. lemma OAI.CurrentProjection.ae_pi_snoc line 200
  19. lemma OAI.CurrentProjection.measurableSet_gramSchmidt_ne_zero line 226
  20. lemma OAI.CurrentProjection.orthonormal_gaussian_map line 242
  21. lemma OAI.CurrentProjection.gaussianReal_le_volume line 267
  22. lemma OAI.CurrentProjection.measure_pi_mono line 284
  23. lemma OAI.CurrentProjection.pi_gaussianReal_le_volume line 297
  24. lemma OAI.CurrentProjection.gaussian_pairings_le line 300
  25. lemma OAI.CurrentProjection.measure_pi_smul line 339
  26. lemma OAI.CurrentProjection.gaussian_rows_pairings_le line 351
  27. lemma OAI.CurrentProjection.lintegral_fin_prod line 368
  28. lemma OAI.CurrentProjection.lintegral_pow_pi line 379