Geodesic
Second derivatives of convex functions in the sense of A.\,D.~Aleksandrov on infinite-dimensional spaces with measure
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 488-504

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We consider convex functions on infinite-dimensional spaces equipped with measures. Our main results give some estimates of the first and second derivatives of a convex function, where second derivatives are considered from two different points of view: as point functions and as measures. 
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     author = {V. I. Bogachev and B. Goldys},
     title = {Second derivatives of convex functions in the sense of {A.\,D.~Aleksandrov} on infinite-dimensional spaces with measure},
     journal = {Matemati\v{c}eskie zametki},
     pages = {488--504},
     publisher = {mathdoc},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a1/}
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V. I. Bogachev; B. Goldys. Second derivatives of convex functions in the sense of A.\,D.~Aleksandrov on infinite-dimensional spaces with measure. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 488-504. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a1/