Geodesic
The class $I_0$ for random increasing upper semicontinuous functions
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 148-151

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Let $C$ be the convex cone $USC_*([0,1],\mathbf{R}_+)$ of increasing upper semicontinuous functions $g\colon[0,1]\to\mathbf{R}_+$. It is shown that the class $I_0(C)$ of distributions on $C$ without indecomposable factor is strictly included in the class of infinitely divisible distributions on $C$.
Keywords: probability measures without indecomposable factor, upper semicontinuous function, infinitely divisible distributions. 
@article{TVP_1999_44_1_a15,
     author = {D. Neuenschwander},
     title = {The class $I_0$ for random increasing upper semicontinuous functions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {148--151},
     publisher = {mathdoc},
     volume = {44},
     number = {1},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a15/}
}
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D. Neuenschwander. The class $I_0$ for random increasing upper semicontinuous functions. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 148-151. http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a15/