Slicing the cube in R n extbf {R}^{n} and probability (bounds for the measure of a central cube slice in R n extbf {R}^{n} by probability methods) Academic Article

A cube of dimension n and side 1 is cut by a hyperplane of dimension n 1 n - 1 through its center. The usual n 1 n - 1 measure of the intersection is bounded between 1 and M, independent of n. The proof uses an inequality for sums of independent random variables.