Théorème de Stone-Weierstrass

'evidence' here are too ill-defined to stand up under such punishment. We should only be depriving them of the very denotations to which they mainly owe such sense as they make to us. It was a lexicographer, Dr. Johnson, who demonstrated the reality of a stone by kicking it; and to begin with, at least, we have little better to go on than Johnsonian usage. The familiar material objects may not be all that is real, but they are admirable examples. There are, however, philosophers who overdo this line of thought

Cependant, il existe des ensembles dont la dimension de a a Hausdorff est non enti`re. De plus, on peut d´montrer que, quelle que soit la dimension e e dH (comprise entre 0 et d), il existe un ensemble de dimension dH . Par exemple, la courbe de Weierstrass ∞ λ(p−2)k cos(πλk t) , W (t) = k=1 t ∈ [0...1] poss`de une dimension de Hausdorff dH ´gale ` p, avec 1 < p < 2 donn´ (ind´pendamment e e a e e de la valeur du param`tre λ > 1). e Sur le plan num´rique, le calcul de la dimension