SET OF EXTREMELY DIRICHLET NON-IMPROVABLE POINTS

Let [Formula: see text] be the continued fraction expansion of [Formula: see text]. The growth rate of the product of the partial quotients [Formula: see text] is closely connected with the improvability of Dirichlet’s theorem in the sense that the faster [Formula: see text] grows, the less possibility the improvement of Dirichlet’s theorem has. In this paper, we study the size of the points for which [Formula: see text] grows in a given speed. We call the points of this type as extremely Dirichlet non-improvable points.