16 авг. 2014 г. · A measure λ on (X×Y,Σ×τ) is said to be a product measure if there exist measures μ,ν on (X,Σ), (Y,τ) respectively, such that λ=μ×ν.

14 февр. 2011 г. · When each ui is totally finite, there is a unique measure on the product measurable space (E,B) of (Ei,Bi,ui). such that "taking measure" and " ...

25 июл. 2013 г. · The product measure would give a probability of 12⋅12 that you get, say, heads on the first coin and tails on the second; the joint distribution ...

29 мар. 2016 г. · Given two measure spaces (X,A,μ) and (Y,B,ν), we can define the product measure μ×ν on the algebra A×B defined as the σ-algebra generated by all ...

16 июл. 2017 г. · Product measures correspond to independence. Specifically, if λ is a measure on ΞN, let X=(X1,…,XN) be a ΞN-valued random variable with law λ.

17 февр. 2016 г. · Independence of two random variables means the joint measure induced by them both can be factorized.

23 июл. 2021 г. · Let's start by remembering that product measures are defined as induced by an outer measure. Therefore, if our two measure spaces are (X,M,μ) ...

9 окт. 2011 г. · For products of non-σ-finite measure spaces it has many desirable properties that the usual product measure lacks. In his Measure Theory, ...

2 февр. 2017 г. · The uniqueness of the product measure is a direct consequence on the following well-known result on the uniqueness of measures:.

2 дек. 2012 г. · These are easily seen to be measurable: ˜f−1(α,∞)=f−1(α,∞)×Y, ˜g−1(α,∞)=X×g−1(α,∞). As h=˜f˜g, it is measurable.