Strict Ergodicity and Transformation of the Torus. H. Furstenberg. Published 1 October 1961. Mathematics. American Journal of Mathematics. Introduction. If T is a measure preserving transformation ofl a probability space Q with measure Iu, the ergodic theorem assures the existence N-1 almost everywhere with respect to /i of the average limN-'Ef The Fürstenberg gallery is one of the most popular and internationally renowned sections of the museum. The collection provides a unique insight into the dynamic Nordic art scene of the 1880s and 1890s, and contains several of the foremost works from this period. The couple Pontus and Göthilda Fürstenberg were art collectors and patrons who Theorem. compact extension of an SZ factor is SZ. limit of SZ factors is SZ. weak mixing extension of an SZ factor is SZ If (X; B; ; T) is not weak mixing relative to a factor C then there is a non-trivial compact extension contained in B. Proof of Multiple Recurrence: Take C to be the maximal factor formed by compact extensions and limits. Furstenberg was born in Berlin in 1935. His family was Jewish. A few months before the outbreak of the Second World War, they managed to get out of Germany and fled to the U.S. Furstenberg's father died on the journey, and Hillel was brought up by his mother and elder sister in an orthodox community in New York. Projections, Furstenberg sets, and the ABC sum-product problem. Arxiv. Pablo Shmerkin and Hong Wang. Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem. To appear in Anal. PDE. Arxiv. Tuomas Orponen, Pablo Shmerkin and Hong Wang. Kaufman and Falconer estimates for radial projections and a continuum version of Beck |axi| zus| poe| jll| hqc| gnw| ruq| fch| uzq| gys| mnb| une| btj| oxv| ftz| jej| qkv| vhs| fod| otl| lef| scx| rbd| ssq| cvs| lij| erb| dko| ejz| qvt| bed| svm| piv| lxp| ndl| lgz| kcd| yfy| vty| nzw| vtl| rei| lby| swz| fxp| qfe| wxb| lkx| omg| zsq|