Abstract
In this paper we prove that for any absolute continuous Borel probability measure μ on the sphere S2 and any t ϵ [0, ] there exist four great semi-circles ℯ1,...,ℯ4 emanating from a point x ϵ S2 that partition sphere S2 into four angular sectors σ1,..., σ4, counter clockwise oriented, such that μ(σ1) = μ(σ4) = t, μ(σ2) = μ(σ3) = - t, and area (σ1) = area(σ4), area(σ2) = area(σ3).
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