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Corrigendum to "On the geometry of metric measure spaces. I." Acta Math. 196 (2006)

Karl-Theodor Sturm

Abstract

This is a corrigendum to Acta Math. 196 (2006) as well as to the follow-up publications JFA 259 (2010) and to JFA 260 (2011).

Corrigendum to "On the geometry of metric measure spaces. I." Acta Math. 196 (2006)

Abstract

This is a corrigendum to Acta Math. 196 (2006) as well as to the follow-up publications JFA 259 (2010) and to JFA 260 (2011).
Paper Structure (5 sections, 1 theorem, 2 equations)

This paper contains 5 sections, 1 theorem, 2 equations.

Table of Contents

  1. The previous erroneous proofs
  2. The corrected statements are derived as follows:
  3. (a) Infinitesimally Hilbertian spaces.
  4. (b) Smooth Finslerian spaces.
  5. References

Key Result

Theorem 1

In the formulations of the Tensorization Property for the assumption non-branching has to be replaced by the stronger assumption that all the metric measure spaces $({\sf M}_i,{\sf d}_i,{\sf m}_i)$ for $i=1,\ldots,\ell$ are

Theorems & Definitions (1)

  • Theorem