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Relations between shy sets and sets of v[p]-measure zero in Solovay's model

Pantsulaia G.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 1

63-69

An example of a non-zero non-atomic translation-invariant Borel measure V[p] on the Banach space l[p] (1 is less than or equal to p is less than or equal to infinity) is constructed in Solovay's model. It is established that, for 1 is less than or equal to p is less than or equal to infinity, the condition "v[p]-almost every element of l[p] has a property P" implies that "almost every" element of l[p] (in the sense of [4]) has the property P. It is also shown that the converse is not valid.