Geodesic
Representation of Functions as Weierstrass- Transforms
Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 711-722

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The Weierstrass - respectively Weierstrass - Stieltjes transform of a function F(t) or μ(t) is defined by 1.1 and 1.2 for all x for which these integrals converge. In what follows we shall always assume that F(t) is Lebesgue integrable in every finite interval and that μ(t) is a function of bounded variation. 
Heinig, H.P. Representation of Functions as Weierstrass- Transforms. Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 711-722. doi: 10.4153/CMB-1967-073-1
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     author = {Heinig, H.P.},
     title = {Representation of {Functions} as {Weierstrass-} {Transforms}},
     journal = {Canadian mathematical bulletin},
     pages = {711--722},
     year = {1967},
     volume = {10},
     number = {5},
     doi = {10.4153/CMB-1967-073-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-073-1/}
}
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