Practical version of the Asymptotic Linearity Theorem with applications to the additivity problems of thermodynamic quantities

By using fundamental notions and theorems of the Lesbesgue integral, a practical version of the Asymptotic Linearity Theorem has been derived. From this new version of the theorem, it easily follows that the theorem is also applicable to the additivity problems of thermodynamic quantities of molecules having many identical moieties, as well as to those of the zero-point vibrational energy of hydrocarbons and the total pi electron energies of altemant hydrocarbons.On leave from: Institute for Fundamental Chemistry, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606, Japan.