I. The Foundation of Measure Theory
II. Integration
III. Construction and Extension of Measures
IV. Kernels and Products of Measures
V. Riesz Spaces and Signed Measures
VI. The Lp Spaces
VII. Measures on a Topological Space
VIII. Convergence and Uniform Integrability
IX. Weak Convergence of Probability Measures
X. Disintegration of Measures
XI. Lebesgue Measure
XII. Hausdorff Measures
Biography
Andrea Carpignani graduated summa cum laude in Mathematics at the University of Pisa in March 2005. He is a member of the London Mathematical Society and a fellow of the Royal Statistical Society. His academic interests are measure theory and integration, convex and functional analysis, probability theory, mathematical statistics, and data science. Following a few years as a teaching assistant at the University of Pisa, he pursued a career in secondary and further education, teaching Mathematics and Physics in Italy and in the UK, where he is currently KS5 Maths Coordinator at The Radcliffe School, in Milton Keynes. Alongside his teaching activity, Andrea Carpignani continues his studies in mathematics focusing on measure theory, algebraic structures and functional analysis.
