Nontangential limit ($\angle {\lim }_{z\to 0}f(z)$)

A boundary limit taken while approaching within a cone that stays away from tangency. At zero in the complex upper half-plane, every fixed cone $|\mathrm{Re}z|\le A\mathrm{Im}z$ is allowed. A nontangential limit need not be a limit along all paths approaching the boundary.

// Destination: analysis.bigb

A fixed-aperture approach region at a boundary point of the unit disc. Its points approach the boundary point without becoming tangent to the circle. Convergence inside every such fixed region is a nontangential limit; the corresponding supremum defines a non-tangential maximal function.