Andres Uribe-Zapata: Finitely additive measures on Boolean algebras: freeness and integration
04/06/24 12:09
Tuesday, June 4, 2024 17:15
Location: A.4.1 C-19
Speaker: Andres Uribe-Zapata (TU Wien)
Title: Finitely additive measures on Boolean algebras: freeness and integration
Abstract: In this talk, we present an integration theory with respect to finitely additive measures on a field of sets \(\mathcal{B} \subseteq \mathcal(X)\) for some non-empty set \(X\). For this, we start by reviewing some fundamental properties of finitely additive measures on Boolean algebras. Later, we present a definition of the integral in this context and some basic properties of the integral and the integrability. We also study integration over subsets of \(X\) to introduce the Jordan algebra and compare the integration on this new algebra with the integration on \(\mathcal{B}\). Finally, we say that a finitely additive measure on \(\mathcal{B}\) is free if \(\mathcal{B}\) contains any finite subset of \(X\) and its measure is zero. We close the talk by providing some characterizations of free finitely additive measures.
This is a joint work with Miguel A. Cardona and Diego A. Mejía.
References:
[CMU] Miguel A. Cardona, Diego A. Mejía and Andrés F. Uribe-Zapata. Finitely additive measures on Boolean algebras. In Preparation.
[UZ23] Andrés Uribe-Zapata. Iterated forcing with finitely additive measures: applications of probability to forcing theory. Master’s thesis, Universidad Nacional de Colombia, sede Medellín, 2023. https://shorturl.at/sHY59.
Location: A.4.1 C-19
Speaker: Andres Uribe-Zapata (TU Wien)
Title: Finitely additive measures on Boolean algebras: freeness and integration
Abstract: In this talk, we present an integration theory with respect to finitely additive measures on a field of sets \(\mathcal{B} \subseteq \mathcal(X)\) for some non-empty set \(X\). For this, we start by reviewing some fundamental properties of finitely additive measures on Boolean algebras. Later, we present a definition of the integral in this context and some basic properties of the integral and the integrability. We also study integration over subsets of \(X\) to introduce the Jordan algebra and compare the integration on this new algebra with the integration on \(\mathcal{B}\). Finally, we say that a finitely additive measure on \(\mathcal{B}\) is free if \(\mathcal{B}\) contains any finite subset of \(X\) and its measure is zero. We close the talk by providing some characterizations of free finitely additive measures.
This is a joint work with Miguel A. Cardona and Diego A. Mejía.
References:
[CMU] Miguel A. Cardona, Diego A. Mejía and Andrés F. Uribe-Zapata. Finitely additive measures on Boolean algebras. In Preparation.
[UZ23] Andrés Uribe-Zapata. Iterated forcing with finitely additive measures: applications of probability to forcing theory. Master’s thesis, Universidad Nacional de Colombia, sede Medellín, 2023. https://shorturl.at/sHY59.