On the Lebesgue decomposition for non-additive functions

Paolo de Lucia passed away on March 18, 2022 in Nyon, Switzerland. He was undoubtedly one of the most respected experts on Real Analysis and Measure Theory, but most of us miss him first of all as a scientific role model, colleague and fatherly friend. Last year, some of his coauthors, students and friends attended the ‘Abstract Measure Theory and Applications: a symposium remembering Paolo de Lucia’s contributions’, held in Naples on March 30–31, 2023, and contributed orally with lectures and speeches in the section ‘Memories’. For this reason, this year we wish to commemorate him by transcribing our two contributions and keeping them unchanged, albeit without the familiar context of the symposium, because unchanged is the sorrow for his loss and the weight of his absence for those who knew him. So, despite an unbridgeable distance, we can imagine him blushing slightly, smiling and saying ironically “At last, for me even a jurist agrees to publish in a mathematics journal”.

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On the Lebesgue decomposition for non-additive functions

Abstract: A Lebesgue decomposition theorem for non-additive functions, acting on a sigma-complete orthomodular lattice and taking values in Hausdorff uniform spaces, is established. No algebraic structure is required on target spaces. The Boolean case is also investigated

Cited by 2 publications

References 11 publications

Boundedness of Nonadditive Quantum Measures

Boundedness of Nonadditive Quantum Measures

In memory of Paolo

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