A note on topological dimension, Hausdorff measure, and rectifiability

Dimension Theory

W Hurewicz and H Wallman · 1941

Earlier work this paper cites.

Modern dimension theory

J Nagata · 1983

Earlier work this paper cites.

Quantitative rectifiability and Lipschitz mappings

G. David and S. Semmes · 1993

Earlier work this paper cites.

Rectifiable metric spaces: local structure and regularity of the Hausdorff measure

B. Kirchheim · 1994

Earlier work this paper cites.

Finding structure in sets with little smoothness

S.. Semmes · 1995

Earlier work this paper cites.

Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities

S. Semmes · 1996

Earlier work this paper cites.

On the nonexistence of bi-Lipschitz parameterizations and geometric problems about A ∞ A_{\infty} -weights

S. Semmes · 1996

Cited alongside, same era.

“Fractured fractals and broken dreams”, volume 7 of Oxford Lecture Series in Mathematics and its Applications

G. David and S. Semmes · 1997

Cited alongside, same era.

Checkerboards, Lipschitz functions and uniform rectifiability

P. W. Jones, N. H. Katz, and A. Vargas · 1997

Cited alongside, same era.

Uniform rectifiability and quasiminimizing sets of arbitrary codimension

G. David and S. Semmes · 2000

Cited alongside, same era.

“Lectures on analysis on metric spaces”

J. Heinonen · 2001

Cited alongside, same era.

Rigidity for quasi-Möbius group actions

M. Bonk and B. Kleiner · 2002

Cited alongside, same era.

Plane with A ∞ A_{\infty} -weighted metric not bi-Lipschitz embeddable to ℝ N {\mathbb{R}}^{N}

T. Laakso · 2002

Later among the works it cites.

Subsets of rectifiable curves in Hilbert space—the analyst’s TSP

R. Schul · 2007

Later among the works it cites.

Weak convergence of currents and cancellation

C. Sormani and S. Wenger · 2010

Later among the works it cites.

Bi-Lipschitz pieces between manifolds

G. C. David · 2016

Later among the works it cites.

Purely unrectifiable metric spaces and perturbations of Lipschitz functions

Original

D. Bate · 2017

Later among the works it cites.

The Besicovitch-Federer projection theorem is false in every infinite-dimensional Banach space

D. Bate, M. Csörnyei, and B. Wilson · 2017