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 Émery-Stricker on Gaussian semimartingales
Keywords: BimeasuresNature: Original
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