We survey results about Haar null subsets of (not necessarily locally compact) Polish
groups. The aim of this paper is to collect the fundamental properties of the various possible …

Abstract Let $ K\subseteq\mathbb {R} $ be a non-empty compact set, and denote by C (K)
the family of all real valued continuous functions on K. The main goal of this paper is to …

Let K be an uncountable compact metric space and let CK; Rd/denote the set of continuous
maps f WK! Rd endowed with the maximum norm. The goal of this paper is to determine …

A set is shy or Haar null (in the sense of Christensen) if there exists a Borel set and a Borel
probability measure μ on C [0, 1] such that and for all f∈ C [0, 1]. The complement of a shy …

We study the level sets of prevalent H\" older functions. For a prevalent $\alpha $-H\" older
function on the unit interval, we show that the upper Minkowski dimension of every level set …

Ce mémoire s' intéresse à des notions de généricité définies sur des espaces vectoriels de
dimension quelconque. Le but est donc de formaliser la notion d'ensemble petit sans faire …

Additive decomposition of a continuous real-valued function on the unit interval in the
framework of fractal dimensions of the graphs of the summands has received significant …

If X is an analytic metric space satisfying a very mild doubling condition, then for any finite
Borel measure μ on X there is a set N⊆ X such that μ (N)> 0, an ultrametric space Z and a …

Let $\ell_1,\ell_2,\dots $ be a countable collection of lines in ${\mathbb R}^ d $. For any $ t\in
[0, 1] $ we construct a compact set $\Gamma\subset {\mathbb R}^ d $ with Hausdorff …

In this paper, we consider the algebraic genericity of continuous functions in terms of
Hausdorff and box dimensions. More precisely, we show that, given s∈(1, 2], the set of …