Riemann average truth-value of Łukasiewicz formulas
Vincenzo Marra, Daniele Mundici · Czech digital mathematics library · 2006
We give a purely algebraic necessary and sufficient condition for a finitely additive measure on a finitely generated free MV-algebra to coincide with the Riemann integral.1. Preliminaries: states, spectra, bases and statement of main resultsIntuitively, a finitely additive measure in Lukasiewicz infinite-valued propositional logic is a method to measure the average truth-value (p of any formula ip.Since ip must only depend on the meaning of </?, any such averaging map ~ is defined on Lindenbaum algebras of formulas, i.e., on MV-algebras.In [6] finitely additive measures on MV-algebras were investigated using the following termi nology: