  A set $\Omega$, of Lebesgue measure 1, in the real line is called spectral if
there is a set $\Lambda$ of real numbers such that the exponential functions
$e_\lambda(x) = \exp(2\pi i \lambda x)$ form a complete orthonormal system on
$L^2(\Omega)$. Such a set $\Lambda$ is called a spectrum of $\Omega$. In this
note we present a simplified proof of the fact that any spectrum $\Lambda$ of a
set $\Omega$ which is finite union of intervals must be periodic. The original
proof is due to Bose and Madan.
