OAI/Analysis/CircleDomains/Sobolev/RectangleDerivativeRepresentatives.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

Measurable representatives of the two ACL derivatives in a physical rectangle. The null set is chosen before slicing, and exceptional lines are discarded only after applying Fubini.

  1. theorem OAI.CircleDomainRigidity.ae_mem_Ioo_of_Icc line 21
  2. theorem OAI.CircleDomainRigidity.lineDeriv_horizontal line 28
  3. theorem OAI.CircleDomainRigidity.lineDeriv_vertical line 35
  4. theorem OAI.CircleDomainRigidity.exists_measurable_horizontal_derivative line 42
  5. theorem OAI.CircleDomainRigidity.exists_measurable_vertical_derivative line 75