1 citations · 3 across the 6 of their papers we have counts for
6 papers
On the validity of Tonelli's Theorem
Paolo Roselli, Michel Willem
This work analyzes the validity of Tonelli's theorem, overcoming the traditional assumption of -finiteness. We prove that the existence and equality of iterated integrals for in…
On the validity of the Radon-Nikodym Theorem
Paolo Roselli, Michel Willem
This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure a…
The surface tangent paradox and the difference vector quotient of a secant plane
Paolo Roselli
If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of seca…
The local Schwarz paradox and the gradient of strongly differentiable functions
Paolo Roselli
We show that the gradient of a multi-variable strongly differentiable function at a point is the limit of a single coordinate-free Clifford quotient between a multi-difference pseu…
The convergence of a gesture recognizer and the shape of a plane gesture
Lorenzo Luzzi, Paolo Roselli
In this work we develop the mathematical framework of !FTL, a new gesture recognition algorithm and we prove its convergence. Such convergence suggests to adopt a notion of shape f…
Algorithms, unaffected by the Schwarz paradox, approximating tangent planes and area of smooth surfaces via inscribed triangular polyhedra
Paolo Roselli
In this work we provide an algorithm approximating the tangent bivector at a point of a smooth surface through inscribed triangles converging to the point, regardless their form or…