Multivariate Chebyshev inequality in generalized measure space based on Choquet integral

ABSTRACT

The multivariate Chebyshev inequality for a random vector on probability measure space has been studied by numerous authors. One thing that seems missing is the multivariate version of Chebyshev inequality in non additive cases. In this article, we show that this inequality still works in generalized probability theory based on Choquet integral.

KEYWORDS:

• Capacity
• Choquet integral
• multivariate Chebyshev inequality

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15