Geodesic
On a characterization of certain families of measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 134-136 
Yu. A. Davydov; A. L. Rozin. On a characterization of certain families of measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 134-136. http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a9/
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     author = {Yu. A. Davydov and A. L. Rozin},
     title = {On a~characterization of certain families of measures},
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     pages = {134--136},
     year = {1978},
     volume = {23},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $(\xi_t)$, $t\in[0,1]$, be a measurable stochastic process. Put $$ \mu_t(A)=\int_0^t 1_A(\xi_s)\,ds\qquad A\in\mathscr B, $$ where $\mathscr B$ is the Borel $\sigma$-algebra in $R^1$. It is easy to see that the family has the following two properties: 1) for any $A\in\mathscr B$ the function $t\rightsquigarrow\mu_t(A)$ is non-decreasing; 2) for any $t\in[0,1]$, $\mu_t(R^1)=t$. We give a characterization of families $(\mu_t)$, with properties 1) and 2), which are generated by a stochastic process.