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The value of a function $f ( z)$, defined on the unit disc $D = \{ {z \in \mathbf C } : {| z | < 1 } \}$, at a boundary point $\zeta = e ^ {i \theta }$, equal to the limit

$$\lim\limits _ {r \uparrow 1 } f ( r e ^ {i \theta } ) \ = f ^ { * } ( e ^ {i \theta } )$$

of the function $f ( z)$ on the set of points of the radius $H = \{ {z = r e ^ {i \theta } } : {0 < r < 1 } \}$ leading to the point $\zeta$. The term "radial boundary value" is sometimes used in a generalized sense for functions $f ( z)$ given on arbitrary (including multi-dimensional) domains $D$, where $H$ is taken to be the set of points of a normal (or its analogue) to the boundary of $D$ leading to the boundary point. For example, in the case of a bi-disc

$$D = \{ {( z _ {1} , z _ {2} ) \in \mathbf C ^ {2} } : { | z _ {1} | < 1 , | z _ {2} | < 1 } \} ,$$

as the radial boundary value at $\zeta = ( e ^ {i \theta _ {1} } , e ^ {i \theta _ {2} } )$ one takes the limit

$$\lim\limits _ {r \uparrow 1 } \ f ( r e ^ {i \theta _ {1} } , r e ^ {i \theta _ {2} } ) = \ f ^ { * } ( \zeta ) .$$

#### References

 [1] A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) (Translated from Russian) [2] I.I. [I.I. Privalov] Priwalow, "Randeigenschaften analytischer Funktionen" , Deutsch. Verlag Wissenschaft. (1956) (Translated from Russian)