Weakly tight functions, their Jordan type decomposition and total variation in effect algebras (Q924117)

The authors introduce and study the notion of a weakly tight function on an effect algebra and present a Jordan-type decomposition theorem for locally bounded real-valued weakly tight functions. Further, they study total variation and \(m\)-atoms for a function \(m\) on a sub-effect algebra and prove that a real-valued additive function defined on a sub-effect algebra is non-atomic iff its total variation is non-atomic.