11 citations · 23 across the 9 of their papers we have counts for
11 papers
A note on Rainwater's Theorem
David Preiss
We extend Rainwater's theorem that, for Baire measures on a compact Hausdorff space,a measure singular with respect to any measure from a -compact convex set of probabilit…
Monotonically controlled integrals
Thomas Ball, David Preiss
The monotonically controlled integral defined by Bendová and Malý, which is equivalent to the Denjoy-Perron integral, admits a natural parameter thereby leading to the whole…
Cone unrectifiable sets and non-differentiability of Lipschitz functions
Olga Maleva, David Preiss
We provide sufficient conditions for a set to be a non-universal differentiability set, i.e. to be contained in the set of points of non-differentiability of…
Differentiability of Lipschitz Functions in Lebesgue Null Sets
David Preiss, Gareth Speight
We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with…
Knot points of typical continuous functions
David Preiss, Shingo Saito
It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strong…
A one-dimensional variational problem with continuous Lagrangian and singular minimizer
Richard Gratwick, David Preiss
We construct a continuous Lagrangian, strictly convex and superlinear in the third variable, such that the associated variational problem has a Lipschitz minimizer which is non-dif…