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1998β€’Transactions of the American Mathematical SocietyOpen access

Baire and 𝜎-Borel characterizations of weakly compact sets in 𝑀(𝑇)

T. V. Panchapagesan

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Abstract

Let T T be a locally compact Hausdorff space and let M ( T ) M(T) be the Banach space of all bounded complex Radon measures on T T . Let B o ( T ) \mathcal {B}_o(T) and B c ( T ) \mathcal {B}_c(T) be the Οƒ \sigma -rings generated by the compact G Ξ΄ G_\delta subsets and by the compact subsets of T T , respectively. The members of B o ( T ) \mathcal {B}_o(T) are called Baire sets of T T and those of B c ( T ) \mathcal {B}_c(T) are called Οƒ \sigma -Borel sets of T T (since they are precisely the Οƒ

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Let T T be a locally compact Hausdorff space and let M ( T ) M(T) be the Banach space of all bounded complex Radon measures on T T . Let B o ( T ) \mathcal {B}_o(T) and B c ( T ) \mathcal {B}_c(T) be the Οƒ \sigma -rings generated by the compact G Ξ΄ G_\delta subsets and by the compact subsets of T T , respectively. The members of B o ( T ) \mathcal {B}_o(T) are called Baire sets of T T and those of B c ( T ) \mathcal {B}_c(T) are called Οƒ \sigma -Borel sets of T T (since they are precisely the Οƒ

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Available abstract

Let T T be a locally compact Hausdorff space and let M ( T ) M(T) be the Banach space of all bounded complex Radon measures on T T . Let B o ( T ) \mathcal {B}_o(T) and B c ( T ) \mathcal {B}_c(T) be the Οƒ \sigma -rings generated by the compact G Ξ΄ G_\delta subsets and by the compact subsets of T T , respectively. The members of B o ( T ) \mathcal {B}_o(T) are called Baire sets of T T and those of B c ( T ) \mathcal {B}_c(T) are called Οƒ \sigma -Borel sets of T T (since they are precisely the Οƒ

Key concepts: Mathematics, Borel equivalence relation, Locally compact space, Bounded function, Hausdorff space, Banach space, Polish space, Borel set

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Baire and 𝜎-Borel characterizations of weakly compact sets in 𝑀(𝑇) β€” Research Paper | ScholarLens