Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 275-304

ON THE RELATIONSHIP BETWEEN DERIVATIONS AND MEASURABLE DIFFERENTIABLE STRUCTURES

Andrea Schioppa

New York University, Courant Institute, Department of Mathematics
251 Mercer St., New York, NY 10012, U.S.A.; schioppa 'at' cims.nyu.edu

Abstract. We study the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove:

(1) the existence of a measurable differentiable structure assuming that one can control the pointwise upper Lipschitz constant of a function through derivations;

(2) an extension of a result of Keith about the choice of chart functions.

2010 Mathematics Subject Classification: Primary 53C23, 46J15.

Key words: Measurable differentiable structure, Rademacher Theorem, derivation, Lipschitz algebra.

Reference to this article: A. Schioppa: On the relationship between derivations and measurable differentiable structures. Ann. Acad. Sci. Fenn. Math. 39 (2014), 275-304.

Full document as PDF file

doi:10.5186/aasfm.2014.3910