Limits of integrals involving almost periodic functions

"Let ${ m Sp}subset{Bbb R}^+$ be a discrete countable set, ${a_lambda}_{lambdain m Sp}$ be a sequence in $l^1( m Sp)$ and $f(x)coloneqsum_{lambdain m Sp}a_lambdasin(lambda x)$. Then $f$ is an almost periodic odd function with ${lambdacolon±lambdain m Sp}$ as spectrum. We give some conditions about the set $S$ so that $int^{+infty}_1f(x)sin(Rx){dxover x} o0$ whenever $R o+infty, Rin S$."