Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Topology in PVS: continuous mathematics with applications
Proceedings of the second workshop on Automated formal methods
Local Theory Specifications in Isabelle/Isar
Types for Proofs and Programs
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Formal probabilistic analysis of cyber-physical transportation systems
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
Improving real analysis in coq: a user-friendly approach to integrals and derivatives
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
MaSh: machine learning for sledgehammer
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Type classes and filters for mathematical analysis in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
| Hi-index | 0.00 |
Currently published HOL formalizations of measure theory concentrate on the Lebesgue integral and they are restricted to realvalued measures. We lift this restriction by introducing the extended real numbers. We define the Borel s-algebra for an arbitrary type forming a topological space. Then, we introduce measure spaces with extended real numbers as measure values. After defining the Lebesgue integral and verifying its linearity and monotone convergence property, we prove the Radon-Nikodým theorem (which shows the maturity of our framework). Moreover, we formalize product measures and prove Fubini's theorem. We define the Lebesgue measure using the gauge integral available in Isabelle's multivariate analysis. Finally, we relate both integrals and equate the integral on Euclidean spaces with iterated integrals. This work covers most of the first three chapters of Bauer's measure theory textbook.