Lp simulation for measures

Being motivated by general interest as well as by certain concrete problems of Fourier Analysis, we construct analogs of the Lp spaces for measures. It turns out that most of standard properties of the usual Lp spaces for functions are extended to the measure setting. We illustrate the obtained results by examples and apply them to obtain a version of the uncertainty principle and an integrability result for the Fourier transform of a function of bounded variation.