The packing measure for a random re-ordering of the Cantor set, the packing dimension for the random set belonging to a sequence satisfying the Hausdorff and packing measures and packing measures for random subsets of...The packing measure for a random re-ordering of the Cantor set, the packing dimension for the random set belonging to a sequence satisfying the Hausdorff and packing measures and packing measures for random subsets of R belonging to a regular sequence have been obtained.展开更多
Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variabl...Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variables on （Ω, F, P） with X<sub>n</sub>（ω）=ω<sub>n</sub>, where ω=（ω<sub>1</sub>, ω<sub>2</sub>,…）. The {X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given展开更多
In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure...In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.展开更多
文摘The packing measure for a random re-ordering of the Cantor set, the packing dimension for the random set belonging to a sequence satisfying the Hausdorff and packing measures and packing measures for random subsets of R belonging to a regular sequence have been obtained.
文摘Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variables on （Ω, F, P） with X<sub>n</sub>（ω）=ω<sub>n</sub>, where ω=（ω<sub>1</sub>, ω<sub>2</sub>,…）. The {X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given
文摘In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.
