A quasiconvex function f being given, does there exist an increasing and continuous k which makes $$k\circ f$$ convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor concavifiable. Finally, some considerations the approximation preorder from finite number observations revealed preference problem are d...

If 1(t) is odd about several points (xe , I (x,)) it is to be understood that the exceptional set may depend on x a . BOAS 1) proves among others that if 1(t) is periodic, bounded on a set of positive measure, and satisfies (1) for a set of x's having positive measure then 1(t) is equivalent to a constant (i .e . 1(t) is constant almost everywhere) . He also shows there exists a bounded periodi...

1. Let G be a locally compact and abelian group, Gl the dual group. Through this paper, "Ml will denote the set of all bounded Radon measure n on G; this set will be considered as a Banach algebra when provided with the customary norm as the dual of the space Co(G) defined below and with the ring product defined as convolution. If /iGM1, its Fourier transform is by definition the bounded and co...

Question 1. Let f(z1, . . . , zn) be a holomorphic function on an open set U ⊂ C. For which t ∈ R is |f |t locally integrable? The positive values of t pose no problems, for these |f |t is even continuous. If f is nowhere zero on U then again |f |t is continuous for any t ∈ R. Thus the question is only interesting near the zeros of f and for negative values of t. More generally, if h is an inve...