*Accepted Paper*

**Inserted:** 19 apr 2013

**Last Updated:** 15 jul 2013

**Journal:** J. Reine Angew. Math.

**Year:** 2013

**Abstract:**

We show that in any infinitesimally Hilbertian $CD^*(K,N)$-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian $CD^*(0,N)$-spaces.

**Tags:**
GeMeThNES

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