Gunturk, BanuCengiz, Bahaettin2019-05-042019-05-0420181300-0098http://journals.tubitak.gov.tr/math/issues/mat-18-42-5/mat-42-5-16-1705-119.pdfhttp://hdl.handle.net/11727/3132This paper is devoted to hyperstonean spaces that are precisely the Stone spaces of measure algebras, or the Stone spaces of the Boolean algebras of L-p-projections of Banach spaces for 1 <= p < infinity, p not equal 2. Several new results that have been achieved recently are discussed. Among these, in our opinion, the most significant one is that which states that any Bochner L-p space is the p-direct sum of Bochner L-p-spaces of perfect regular Borel measures on Stonean spaces for 1 <= p < infinity. Overall, we try to shed some light on the inner structure of these spaces, about which very little is known.enginfo:eu-repo/semantics/openAccessStonean spacePerfect measureEquivalent measuresBochner spacep-direct sumArticle425228822950004479468000162-s2.0-85054817331