  The base-$k$ {\em Copeland-Erd\"os sequence} given by an infinite set $A$ of
positive integers is the infinite sequence $\CE_k(A)$ formed by concatenating
the base-$k$ representations of the elements of $A$ in numerical order. This
paper concerns the following four quantities.
  The {\em finite-state dimension} $\dimfs (\CE_k(A))$, a finite-state version
of classical Hausdorff dimension introduced in 2001.
  The {\em finite-state strong dimension} $\Dimfs(\CE_k(A))$, a finite-state
version of classical packing dimension introduced in 2004. This is a dual of
$\dimfs(\CE_k(A))$ satisfying $\Dimfs(\CE_k(A))$ $\geq \dimfs(\CE_k(A))$.
  The {\em zeta-dimension} $\Dimzeta(A)$, a kind of discrete fractal dimension
discovered many times over the past few decades.
  The {\em lower zeta-dimension} $\dimzeta(A)$, a dual of $\Dimzeta(A)$
satisfying $\dimzeta(A)\leq \Dimzeta(A)$.
  We prove the following.
  $\dimfs(\CE_k(A))\geq \dimzeta(A)$. This extends the 1946 proof by Copeland
and Erd\"os that the sequence $\CE_k(\mathrm{PRIMES})$ is Borel normal.
  $\Dimfs(\CE_k(A))\geq \Dimzeta(A)$.
  These bounds are tight in the strong sense that these four quantities can
have (simultaneously) any four values in $[0,1]$ satisfying the four
above-mentioned inequalities.
