The connectivity of the hydrophobic medium in the nonionic binary system C 12 EO 6 /H 2 O is studied by monitoring the diffusion constants of tracer molecules at the transition between the hexagonal mesophase and the fluid isotropic phase. The increase in the transverse diffusion coefficient on approaching the isotropic phase reveals the proliferation of bridge-like defects connecting the surfactant cylinders. This suggests that the isotropic phase has a highly connected structure. Indeed, we find similar diffusion coefficients in the isotropic and cubic bicontinuous phases. The temperature dependence of the lattice parameter in the hexagonal phase confirms the change in connectivity close to the hexagonal-isotropic transition. Finally, an X-ray investigation of the isotropic phase shows that its structure is locally similar to that of the hexagonal phase.

Abstract. Let S 1 be the stopping time space and B 1 (S 1 ) be the Baire-1 elements of the second dual of S 1 . To each element x * * in the space B 1 (S 1

Abstract. To each function f of bounded quadratic variation we associate a Hausdorff measure μ f . We show that the map f → μ f is locally Lipschitz and onto the positive cone of M[0, 1]. We use the measures {μ f : f ∈ V 2 } to determine the structure of the subspaces of V 0 2 which either contain c 0 or the square stopping time space S 2 .

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