Geodesic
The Cavalieri condition for integrals over $k$-dimensional planes, $k$
Algebra i analiz, Tome 5 (1993) no. 4, pp. 191-205.

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     author = {E. E. Petrov},
     title = {The {Cavalieri} condition for integrals over $k$-dimensional planes, $k<n-1$},
     journal = {Algebra i analiz},
     pages = {191--205},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_1993_5_4_a7/}
}
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E. E. Petrov. The Cavalieri condition for integrals over $k$-dimensional planes, $k