Cauchy's Equation and Sufficient Statistics on Arcwise Connected Spaces
Denny, J. L.
Ann. Math. Statist., Tome 41 (1970) no. 6, p. 401-411 / Harvested from Project Euclid
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We show that a measure-theoretic extension of Cauchy's functional equation, namely, $g(x_1) + g(x_2) = h(f(x_1, x_2))$ a.e., for real-valued functions defined on measure spaces equipped with a "reasonably compatible" arcwise connected topology is equivalent to a theorem which characterizes one-parameter exponential families on such measure spaces in terms of a real-valued sufficient statistic.
Publié le : 1970-04-14
Classification:  
@article{1177697079,
     author = {Denny, J. L.},
     title = {Cauchy's Equation and Sufficient Statistics on Arcwise Connected Spaces},
     journal = {Ann. Math. Statist.},
     volume = {41},
     number = {6},
     year = {1970},
     pages = { 401-411},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177697079}
}

Denny, J. L. Cauchy's Equation and Sufficient Statistics on Arcwise Connected Spaces. Ann. Math. Statist., Tome 41 (1970) no. 6, pp.  401-411. http://gdmltest.u-ga.fr/item/1177697079/