A uniform distribution on a high-dimensional space R^n can be defined with a density function that is 1 within the n-dimensional unit cube and 0 outside of it. This means that every point within the unit cube has an equal probability of being selected, while points outside the cube have zero probability. The discussion emphasizes the simplicity of this definition when constrained to the unit cube, making it a foundational concept in probability theory and high-dimensional statistics.
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