Application of copulas in the proof of the almost sure central limit theorem for the $k$th largest maxima of some random variables

Our aim is to prove the almost sure central limit theorem for the $k$th largest maxima $( M_{n}^{( k) }) $, $k=1,2,\ldots , $ of $X_{1},\ldots ,X_{n}$, $n \gt k$, where $( X_{i}) $ forms a stochastic process of identically distributed r.v.’s of continuous