On some properties of hyperstonean spaces
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This 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.