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• # Artykuł - szczegóły

## Studia Mathematica

2006 | 175 | 2 | 139-155

## Uniqueness of measure extensions in Banach spaces

EN

### Abstrakty

EN
Let X be a Banach space, $B ⊂ B_{X*}$ a norming set and 𝔗(X,B) the topology on X of pointwise convergence on B. We study the following question: given two (non-negative, countably additive and finite) measures μ₁ and μ₂ on Baire(X,w) which coincide on Baire(X,𝔗(X,B)), does it follow that μ₁ = μ₂? It turns out that this is not true in general, although the answer is affirmative provided that both μ₁ and μ₂ are convexly τ-additive (e.g. when X has the Pettis Integral Property). For a Banach space Y not containing isomorphic copies of ℓ¹, we show that Y* has the Pettis Integral Property if and only if every measure on Baire(Y*,w*) admits a unique extension to Baire(Y*,w). We also discuss the coincidence of the two σ-algebras involved in such results. Some other applications are given.

139-155

wydano
2006

### Twórcy

autor
• Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain
autor
• Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain