Strange notation using dollar sign In the paper Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma, the authors Bellare and Neven use notation which looks like left arrow with dollar sign above it.

Authors provide an explanation for one variable:


  $s \overset{{\scriptstyle \$}}{\longleftarrow S}$ denotes the
  operation of assigning to $s$ an element of $S$ chosen at random


However, in this paper they use it with multiple variables like this:


  $s_1, \ldots, s_N \overset{{\scriptstyle \$}}{\longleftarrow S}$


What is the definition of this notation? Can we chose dependent random variables for $s_i$? Do we must choose all variables $(s_1, \ldots, s_N)$ at once from the set $S^N$ with uniform distribution?
$s_1, ..., s_N \stackrel{\$}{\leftarrow} S$

means coordinate-wise sampling:

$s_1 \stackrel{\$}{\leftarrow} S$

$s_2 \stackrel{\$}{\leftarrow} S$

...

$s_N \stackrel{\$}{\leftarrow} S$