ABSTRACT
Let X be a random vector defined on a probability space ( Ω , F , P ) $ (\Omega , \mathcal{{F}}, P) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_1.tif"/> , taking values in a measurable space ( Ω X , F X ) $ (\Omega _{\scriptscriptstyle X}, \mathcal{{F}} _{\scriptscriptstyle X}) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_2.tif"/> . Let X 1 , … , X n $ X _{\scriptscriptstyle 1}, \ldots , X _{\scriptscriptstyle n} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_3.tif"/> be independent copies of X. We assume Ω X $ \Omega _{\scriptscriptstyle X} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_4.tif"/> to be a subset of R p $ \mathbb R ^{\scriptscriptstyle {p}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_5.tif"/> , the p-dimensional Euclidean space, and F X = { Ω X ∩ B : B ∈ R p } $ \mathcal{{F}} _{\scriptscriptstyle X} = \{ \Omega _{\scriptscriptstyle X} \cap B: B \in \mathcal{{R}} ^{\scriptscriptstyle {p}}\} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_6.tif"/> , where R p $ \mathcal{{R}} ^{\scriptscriptstyle {p}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_7.tif"/> is the Borel σ $ \sigma $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_8.tif"/> -field on R p $ \mathbb R ^{\scriptscriptstyle {p}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math1_9.tif"/> .
