Re: Appending lines starting with white space to the previous line reads the entire file into memory. This version processes the file line by line thanks to redo and a one line lookahead.

chomp( my $line = <$fh> );
while (defined($line)) {
   chomp( my $next = <$fh> );
   if (defined($next) && $next =~ s/^\s+//) {
      $line .= $next;
      redo;
   }

   ... do something with $line ...

   $line = $next;
}
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Update: Tested. Small syntax fix.