Type alternative for Frostman measures.

For a finite positive Borel measure μ on R its exponential type, T μ , is defined as the infimum of a > 0 such that finite linear combinations of complex exponentials with frequencies between 0 and a are dense in L 2 (μ). The definition can be easily extended from finite to broader classes of measures. In this paper we prove a new formula for T μ and use it to study growth and additivity properties of measures with finite positive type. As one of the applications, we show that Frostman measures on R may only have type zero or infinity. [ABSTRACT FROM AUTHOR]