Geodesic
An Application of Nonstandard Analysis to Functional Equations
Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 23 .

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Using methods of nonstandard analysis it is proved that all measurable solutions of the equation $f(x+y)=g(f(x),\, f(y),\,\, x, y)$ (with $g$ continuous) are continuous.
Classification : 03H05 39B99 
@article{PIM_1985_N_S_37_51_a3,
     author = {Miodrag Ra\v{s}kovi\'c},
     title = {An {Application} of {Nonstandard} {Analysis} to {Functional} {Equations}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {23 },
     publisher = {mathdoc},
     volume = {_N_S_37},
     number = {51},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a3/}
}
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Miodrag Rašković. An Application of Nonstandard Analysis to Functional Equations. Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 23 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a3/