For infinite-symbol $E$-representation of numbers $x \in (0, 1]$:
  \[
    x = \sum_{n=1}^\infty
      \frac{1}{(2+g_1)\ldots(2+g_1+g_2+\ldots+g_n)}
    \equiv \Delta^E_{g_1g_2\ldots g_n\ldots},
  \]
  where $g_n \in \Z_0 = \{ 0, 1, 2, \ldots \}$,
  we consider a class of $E$-cylinders, i.e.,
  sets defined by equality
  \[
    \Delta^E_{c_1\ldots c_m}
    = \left\{ x \colon x = \Delta^E_{c_1\ldots c_mg_{m+1}\ldots g_{m+k}\ldots}, \;
      g_{m+k} \in \Z_0, \; k \in \N \right\}.
  \]
  We prove that, for determination (calculation)
  of fractal Hausdorff-Besicovitch dimension
  of any Borel set $B \subset [0, 1]$,
  it is enough to use coverings of the set $B$
  by connected unions of $E$-cylinders of the same rank
  that belong to the same cylinder of the previous rank.

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