no. 2
Convergence theorem for riemannian manifolds with boundary
Compositio Mathematica, Tome 75 (1990) no. 2, pp. 171-192 
@article{CM_1990__75_2_171_0,
     author = {Kodani, Shigeru},
     title = {Convergence theorem for riemannian manifolds with boundary},
     journal = {Compositio Mathematica},
     pages = {171--192},
     year = {1990},
     publisher = {Kluwer Academic Publishers},
     volume = {75},
     number = {2},
     mrnumber = {1065204},
     zbl = {0703.53043},
     language = {en},
     url = {https://www.numdam.org/item/CM_1990__75_2_171_0/}
}
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Kodani, Shigeru. Convergence theorem for riemannian manifolds with boundary. Compositio Mathematica, Tome 75 (1990) no. 2, pp. 171-192. https://www.numdam.org/item/CM_1990__75_2_171_0/

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