() can be relaxed to with the same conclusion. Special cases In practice the point 0 is often transformed into the point ∞ of the Riemann sphere. This gives a version of the principle that applies to strips, for example bounded by two lines of constant real part in the complex plane. This special case is sometimes known as Lindelöf's theorem. Carlson's theorem is an application of the principle to functions bounded on the imaginary axis. References (Corr. ) (See chapter 5) Mathematical principles Theorems in complex analysis