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It is proved that      L 1 {L^1}       is isomorphic to a subspace of      L 1 / H 1 {L^1}/{H^1}      . More precisely, there exists a diffuse      σ  \sigma      -algebra      S \mathfrak {S}       on the circle such that the corresponding expectation      E : H ∞  →  L ∞  ( C ) {\mathbf {E}}:{H^\infty } \to {L^\infty }({\mathbf {C}})       is onto. The method consists in studying certain martingales on the product      ∏  N {\prod ^{\mathbf {N}}}      .

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