Dimension Results in Product Probability Spaces

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）.