Around the oscillation theorem on irrationality measure function

In 2010 Kan and Moshchevitin proved a surprising theorem (see https://arxiv.org/abs/0910.2428) on oscillation of the difference for irrationality measure functions of two real numbers. During the last 10 years this theorem has had some generalisations and adjustments. Quite unexpectedly, a serious adjustment was recently obtained by V.Manturov and N.Moshchevitin. I will tell about all these themes in my talk.