Abstract: | Necessary and sufficient conditions are given which ensure the completeness of the trigonometric systems with integer indices; {einx; x
}∞n=−∞ or {einx; x
}∞n=1 in Lα(μ,
), α1. If there exists a support Λ of the measure μ which is a wandering set, that is, Λ+2kπ, k=0, ±1, ±2, … are mutually disjoint for different k's, then the linear span of our trigonometric system {einx; x
}∞n=−∞ is dense in Lα(μ,
) α1. The converse statement is also true. |