"new foundations must give new math"

from "The Basic Picture. Structures for constructive topology"

by Giovanni Sambin, Oxford University Press, forthcoming


To register send an e-mail to maietti @ math.unipd.it

Registration fee: 40 euros
(to be paid at arrival).

Under the patronage of

Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy

University of Padova, Italy

AILA (Italian Association of Logic and Applications), whose first president was Giovanni Sambin (from 1987 to 1994).

Abstracts » Toto

Claudio Sacerdoti Coen

A constructive proof of Lebesgue's Dominated Convergence Theorem for Ordered Uniformities

We present a constructive proof, in the sense of Bishop, of Lebesgue's Dominated Convergence Theorem in the abstract setting of Ordered Uniformities.

The latter mathematical structures are uniformities with an order on their elements. The two structures are linked by an additional hypothesis of convexity.

Under an additional hypothesis on the base of the uniformity, the proof is also fully acceptable in a predicative setting.

Moreover, the proof has been completely formalized in the interactive theorem prover Matita.

The classical counterpart of the proof can be found in Hans Weber's "Uniform Lattices II: Order Continuity and Exhaustivity", in Annali di Matematica Pura ed Applicata (IV), Vol. CLXV (1993).