  M\"untz spaces satisfying the M\"untz and gap conditions are considered. A
Fourier approximation of functions in the M\"untz spaces $M_{\Lambda ,p}$ of
$L_p$ functions is studied, where $1<p<\infty $. It is proved that up to an
isomorphism and a change of variables these spaces are contained in Weil-Nagy's
class. Moreover, existence of Schauder bases in the M\"untz spaces $M_{\Lambda
,p}$ is investigated.
