A disjointness property of l p n sequences in L p
Séminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz") (1978-1979), Exposé no. 21, 13 p. 
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     author = {Schechtman, G.},
     title = {A disjointness property of $l^n_p$ sequences in $L_p$},
     journal = {S\'eminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz")},
     note = {talk:21},
     pages = {1--13},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1978-1979},
     language = {en},
     url = {http://www.numdam.org/item/SAF_1978-1979____A18_0/}
}
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Schechtman, G. A disjointness property of $l^n_p$ sequences in $L_p$. Séminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz") (1978-1979), Exposé no. 21, 13 p. http://www.numdam.org/item/SAF_1978-1979____A18_0/

(1) L.E. Dor, On projections in L1, Ann of Math. 102 (1975), 463 -474. | MR | Zbl

(2) P. Enflo and H.P. Rosenthal, Some results concerning Lp(μ) spaces, J. Funct. Anal. 14(1973), 325-348. | Zbl

(3) G. Schechtman, Almost isometric Lp subspaces of Lp(0,1), to appear in the J. of the London Math. Soc. | Zbl