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XI: 07, 59-64, LNM 581 (1977)

**HOROWITZ, Joseph**

Une remarque sur les bimesures (Measure theory)

A bimeasure is a function $\beta(A,B)$ of two set variables, which is a measure in each variable when the other is kept fixed. It is important to have conditions under which a bimeasure ``is'' a measure, i.e., is of the form $\mu(A\times B)$ for some measure $\mu$ on the product space. This is known to be true for positive bimeasures ( Kingman,*Pacific J. of Math.,* **21**, 1967, see also 315). Here a condition of bounded variation is given, which implies that a bimeasure is a difference of two positive bimeasures, and therefore is a measure

Comment: Signed bimeasures which are not measures occur naturally, see for instance Bakry 1742, and Ă‰mery-Stricker on Gaussian semimartingales

Keywords: Bimeasures

Nature: Original

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Une remarque sur les bimesures (Measure theory)

A bimeasure is a function $\beta(A,B)$ of two set variables, which is a measure in each variable when the other is kept fixed. It is important to have conditions under which a bimeasure ``is'' a measure, i.e., is of the form $\mu(A\times B)$ for some measure $\mu$ on the product space. This is known to be true for positive bimeasures ( Kingman,

Comment: Signed bimeasures which are not measures occur naturally, see for instance Bakry 1742, and Ă‰mery-Stricker on Gaussian semimartingales

Keywords: Bimeasures

Nature: Original

Retrieve article from Numdam