Euclidean space

Metric space

Pure mathematics

Lipschitz continuity

Cover (algebra)

Mathematics

Interpolation space

Gene

Ricci curvature

Engineering

Besov space

Mathematical analysis

Philosophy

Hausdorff dimension

Chemistry

Curvature

Differentiable function

Geometry

Space (punctuation)

Measure (data warehouse)

Computer science

Linguistics

Functional analysis

Bounded function

Biochemistry

Hausdorff measure

Database

Mechanical engineering

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

We prove that, given an RCD * (K, N )-space (X, d, m), then it is possible to m-essentially cover X by measurable subsets (R i ) i∈N with the following property: for each i there exists k i ∈ N ∩ [1, N ] such that m R i is absolutely continuous with respect to the k i -dimensional Hausdorff measure.We also show that a Lipschitz differentiability space which is locally bi-Lipschitz embeddable into euclidean spaces is rectifiable as a metric measure space, and we conclude with an application to Alexandrov spaces.

On the volume measure of non-smooth spaces with Ricci curvature bounded below