MEASURES ON COALLOCATION AND NORMAL LATTICES

JACK-KANG CHAN

《International Journal of Mathematics and Mathematical Sciences》 1992卷 (1992/12) Pp. 701-718

https://doi.org/10.1155/S0161171292000929

摘要

Let L1 and L2 be lattices of subsets of a nonempty set X. suppose L2 coallocates L1 and L1 is a subset of L2 .We show that any ,L1-regular finitely additive measure on the algebra generated by L1 can be uniquely extended to an L2-regular measure on the algebra generated by L2. The case when L1, is not necessary contained in L2, as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.

關鍵字

lattices ； normal lattices ； coallocation lattices ； semi-separated lattices ； regular finitely additive measures ； u-smooth measures ； measure extension ； measure enlargement