Fekete's lemma for componentwise subadditive functions of two or more real variables

We prove an analogue of Fekete's subadditivity lemma for functions several real variables which are subadditive in each variable taken singularly. This extends both the classical case one variable, and a similar result integer variables. While doing so, we that with property mentioned above bounded every closed subset their domain. The arguments expand on those Chapter 6 E. Hille's 1948 textbook.