Suppose that p∈(1, ∞], ν ∈[1/2, ∞), Sν = (x 1 , x 2 )∈R 2 \{(0, 0)}:|φ|< π 2ν , where φ is the polar angle of (x 1 , x 2 ). Let R>0 and ωp(x) be the p-harmonic measure of ∂B(0, R)∩Sν at x with respect to B(0, R)∩Sν . We prove that there exists a constant C such thatwhenever x∈B(0, R)∩S 2ν and where the exponent k(ν, p) is given explicitly as a function of ν and p. Using this estimate we derive local growth estimates for p-sub-and p-superharmonic functions in planar domains which are locally approximable by sectors, e.g., we conclude bounds of the rate of convergence near the boundary where the domain has an inwardly or outwardly pointed cusp. Using the estimates of p-harmonic measure we also derive a sharp Phragmén-Lindelöf theorem for p-subharmonic functions in the unbounded sector Sν . Moreover, if p=∞ then the above mentioned estimates extend from the setting of two-dimensional sectors to cones in R n . Finally, when ν ∈(1/2, ∞) and p∈(1, ∞) we prove uniqueness (modulo normalization) of positive p-harmonic functions in Sν vanishing on ∂Sν .

, where φ is the polar angle of (x, y). Let R > 0 and ω p (x) be the p-harmonic measure of ∂B(0, R) ∩ S v at x with respect to B(0, R) ∩ S v . We prove that there exists a constant C such thatwhere the exponent k(v, p) is given explicitly as a function of v and p. Using this estimate we derive local growth estimates for p-suband p-superharmonic functions in planar domains which are locally approximable by sectors, e.g., we conclude bounds of the rate of convergence near the boundary where the domain has an inwardly or outwardly pointed cusp. Using the estimates of p-harmonic measure we also derive a sharp Phragmen-Lindelöf theorem for p-subharmonic functions in the unbounded sector S v . Moreover, if p = ∞ then the above mentioned estimates extend from the setting of two-dimensional sectors to cones in R n . Finally, when v ∈ (1/2, ∞) and p ∈ (1, ∞) we prove a uniqueness result (modulo normalization) for positive p-harmonic functions in S v vanishing on ∂S v .

A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and Stokes' theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable to higher dimensions.