乘积概率空间中的维数结果

Dimension Results in Product Probability Spaces

摘要: 在R^d₁, R^d₂中的分形测度和R^d₁+r₂ 中乘积测度之间的关系已经被许多作者发展。本文目的是在概率空间（Ω₁,F₁,μ₁）,（Ω₂,F₂,μ₂）和它们的乘积概率空间（Ω₁ x Ω₂,F₁ x F₂, μ₁xμ₂）中对Hausdorff维数和填充维数探索相应的结果。

Abstract: The relationship between fractal measures in R^d₁, R^d₂ and their product measures in R^d₁+d₂ has been developed by many authors. The object of this paper is to explore the corresponding results for Hausdorff dimension and packing dimension in two probability spaces （Ω₁,F₁,μ₁）,（Ω₂,F₂,μ₂） and their product probability space （Ω₁ x Ω₂,F₁ x F₂, μ₁xμ₂）.