Geodesic
On constructive distribution functions
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 59-64

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The concept is introduced of a distribution function given by means of a sequence of finite-step functions that converges in the integral metric. (As shown in [1], the pointwise representation of a constructive distribution function at all points is not possible.) It is shown that there is a correspondence between constructive distributive functions and constructive characteristic functions. 
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     author = {N. K. Kossovski},
     title = {On constructive distribution functions},
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     publisher = {mathdoc},
     volume = {60},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a5/}
}
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N. K. Kossovski. On constructive distribution functions. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 59-64. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a5/