We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In p...We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In particular, we construct translation-invariant extensions of ordinary and standard Lebesgue measures on R∞ and Rogers-Fremlin measures on l∞, respectively, such that topological weights of quasi-metric spaces associated with these measures are maximal （i.e., 2c）. We also solve some Fremlin problems concerned with an existence of uniform measures in Banach spaces.展开更多
基金Supported by National Science Foundation of Georgia （Grants Nos. GNSF/ST 08/3-391, Sh. Rustaveli GNSF/ST 09_144-3-105）
文摘We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In particular, we construct translation-invariant extensions of ordinary and standard Lebesgue measures on R∞ and Rogers-Fremlin measures on l∞, respectively, such that topological weights of quasi-metric spaces associated with these measures are maximal （i.e., 2c）. We also solve some Fremlin problems concerned with an existence of uniform measures in Banach spaces.
