Measure, Integration & Real Analysis · Problem 5C.13

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · volume-unit-ball-gamma-function

Problem

For readers familiar with the gamma function

\Gamma

: Prove that

\lambda_n(\mathbf{B}_n) = \frac{\pi^{n/2}}{\Gamma\!\left(\frac{n}{2} + 1\right)}

for every positive integer

n