Fetching the paper…
Reading the bibliography…
We characterise purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of elements of the set of all bounded 1-Lipschitz functions $f\colon X \to \mathbb R^m$ with respect to the supremum norm.
Incommensurability of the minimal linear measure with the length of a set
A. G. Vituškin, L. D. Ivanov, and M. S. Melnikov · 1963
Earlier work this paper cites.
Rectifiability and integral-geometric measures in homogeneous spaces
J. E. Brothers · 1969
Earlier work this paper cites.
The ( φ , k ) (\varphi,\,k) rectifiable subsets of a homogeneous space
J. E. Brothers · 1969
Earlier work this paper cites.
Geometric measure theory
H. Federer · 1969
Earlier work this paper cites.
Besicovitch-Federer projection theorem for continuously differentiable mappings having constant rank of the Jacobian matrix
J. Gałęski · 1985
Earlier work this paper cites.
Extensions of Lipschitz maps into Banach spaces
W. B. Johnson, J. Lindenstrauss, and G. Schechtman · 1986
Earlier work this paper cites.
Metric space valued functions of bounded variation
L. Ambrosio · 1990
Earlier work this paper cites.
On Besicovitch’s 1 2 \frac{1}{2} -problem
D. Preiss and J. Tišer · 1992
Earlier work this paper cites.
A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov
T. Keleti · 1994
Earlier work this paper cites.
Rectifiable metric spaces: local structure and regularity of the Hausdorff measure
B. Kirchheim · 1994
Earlier work this paper cites.
Geometry of sets and measures in Euclidean spaces
P. Mattila · 1995
Cited alongside, same era.
Differentiability of Lipschitz functions on metric measure spaces
J. Cheeger · 1999
Cited alongside, same era.
Currents in metric spaces
L. Ambrosio and B. Kirchheim · 2000
Cited alongside, same era.
Rectifiable sets in metric and Banach spaces
L. Ambrosio and B. Kirchheim · 2000
Cited alongside, same era.
Structure of null sets in the plane and applications
G. Alberti, M. Csörnyei, and D. Preiss · 2005
Cited alongside, same era.
Differentiability of Lipschitz functions, structure of null sets, and other problems
G. Alberti, M. Csörnyei, and D. Preiss · 2010
Cited alongside, same era.
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
G. Alberti and A. Marchese · 2016
Later among the works it cites.
Topics in Banach space theory
F. Albiac and N. J. Kalton · 2016
Later among the works it cites.
On the structure of 𝒜 \mathcal{A} -free measures and applications
G. De Philippis and F. Rindler · 2016
Later among the works it cites.
A Localized Besicovitch-Federer Projection Theorem, 2016
H. Pugh · 2016
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
Closest in time.
Characterizations of rectifiable metric measure spaces
D. Bate and S. Li · 2017
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Product formulas for measures and applications to analysis and geometry
M. Csörnyei and P. Jones · 2011
Cited alongside, same era.
Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces
R. Hovila, E. Järvenpää, M. Järvenpää, and F. Ledrappier · 2012
Cited alongside, same era.
Structure of measures in Lipschitz differentiability spaces
D. Bate · 2014
Cited alongside, same era.
Transversality of isotropic projections, unrectifiability, and Heisenberg groups, 2014
R. Hovila · 2014
Cited alongside, same era.
Structure of null sets, differentiability of Lipschitz functions, and other problems
G. Alberti, M. Csörnyei, and D. Preiss
Cited in the paper.
Closest in time.
An example pertaining to the failure of the Besicovitch-Federer structure theorem in Hilbert space
T. De Pauw · 2017
Closest in time.
On a conjecture of Cheeger
G. De Philippis, A. Marchese, and F. Rindler · 2017
Closest in time.
A note on topological dimension, Hausdorff measure, and rectifiability, 2018
G. C. David and E. Le Donne · 2018
Closest in time.