Fatou theorem

Target entity: Fatou theorem
Context triple: [Lindelöf theorem in complex analysis, relatedTo, Fatou theorem]

• A. Montel theorem
  Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
• B. Borel–Carathéodory theorem
  The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
• C. Corona theorem
  The Corona theorem is a fundamental result in complex analysis that characterizes when bounded analytic functions on the unit disk can be solved in a certain type of division problem, showing that the maximal ideal space of the disk algebra has no "corona."
• D. Mergelyan's theorem
  Mergelyan's theorem is a fundamental result in complex analysis stating that every function continuous on a compact subset of the complex plane with connected complement and holomorphic in its interior can be uniformly approximated by polynomials.
• E. Picard theorem
  Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Fatou theorem
Target entity description: The Fatou theorem is a fundamental result in complex analysis that describes the almost-everywhere existence of radial boundary limits for bounded analytic (or harmonic) functions on the unit disk.

• A. Montel theorem
  Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
• B. Borel–Carathéodory theorem
  The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
• C. Corona theorem
  The Corona theorem is a fundamental result in complex analysis that characterizes when bounded analytic functions on the unit disk can be solved in a certain type of division problem, showing that the maximal ideal space of the disk algebra has no "corona."
• D. Mergelyan's theorem
  Mergelyan's theorem is a fundamental result in complex analysis stating that every function continuous on a compact subset of the complex plane with connected complement and holomorphic in its interior can be uniformly approximated by polynomials.
• E. Picard theorem
  Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
• F. None of above. chosen