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Valuation and metric on a lattice effect algebra

Khare M., Gupta S.

Demonstratio Mathematica

2008

Vol. 41, nr 2

249-258

In the present paper we have derived some properties of the pseudo-metric introduced by Riećanova on a lattice effect algebra E corresponding to a valuation u on E, which turns out to be a metric if u happens to be faithful. Using these properties we have been able to prove that this metric is complete. Also it is observed that the resulting metric space is convex if and only if w is non-atomic if and only if E is atomless.

Nonatomic vector-valued modular functions

Avallone A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

23-36

We prove a weak Liapunov type theorem for Banach spaces-valued modular functions on complemented lattices.