Geodesic
Sharpness of bounds of stability for Raikov's theorem
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 102-107
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An example is constructed to show that the bounds of stability in the Raikov theorem on the decomposition of the Poisson law cannot be better than $O(\log\log\frac{1}{\varepsilon}/\log\frac{1}{\varepsilon})^2$. 
@article{ZNSL_1976_61_a9,
     author = {J. J. Ma\v{c}ys},
     title = {Sharpness of bounds of stability for {Raikov's} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--107},
     year = {1976},
     volume = {61},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a9/}
}
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J. J. Mačys. Sharpness of bounds of stability for Raikov's theorem. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 102-107. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a9/