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The solutions of incompressible Navier-Stokes equations in four spatialdimensions are considered. We prove that the two-dimensional Hausdorff measureof the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is  added in Remark 1.3. accepted by Comm. Math. Phy

Partial Regularity of Solutions to the Four-Dimensional Navier-Stokes Equations at the First Blow-up Time