Countable tightness in the spaces of regular probability measures

• Autorzy: Grzegorz Plebanek , Damian Sobota
• Języki publikacji: EN

Abstrakty

EN

We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 54C35: Function spaces
• 28A33: Spaces of measures, convergence of measures
• 46E27: Spaces of measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 229
• Numer: 2
• Strony: 159-169

Daty

wydano

2015

Twórcy

autor

Grzegorz Plebanek

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Damian Sobota

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm229-2-4