The random trigonometric series
$$\sum\nolimits_{n = 1}^\infty {{\rho _n}\cos \left( {nt + {\omega _n}} \right)} $$
on the circle
$$\mathbb{T}$$
are studied under the conditions ∑∣ρn∣2 = ∞ and ρn → 0, where {ωn} are independent and uniformly distributed random variables on
$$\mathbb{T}$$
. They are almost surely not Fourier-Stieltjes series but determine pseudo-functions. This leads us to develop the theory of trigonometric multiplicative chaos, which produces a class of random measures. The kernel and t...
