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  • $\begingroup$ Thanks for the notational clarification. Post is duly edited. (Although it seems to me that Susskind refers to the Lagrangian as the Lagrangian density at several points during his online Stanford lectures on GR.) I have also edited the post to modify condition (2) and remove condition (3), which was unnecessary to make my point. Do your comments still apply considering this modification? $\endgroup$ Commented Jan 3, 2013 at 15:57
  • $\begingroup$ I updated the answer. $\endgroup$ Commented Jan 3, 2013 at 20:01