Countably tight dual ball with a nonseparable measure

Abstract We construct a compact Hausdorff space such that the space of Radon probability measures on considered with the topology (induced from the space of continuous functions ) is countably tight that is a generalization of sequentiality (i.e., if a measure is in the closure of a set , there is a countable such that is in the closure of ) but carries a Radon probability measure that has uncountable Maharam type (i.e., is nonseparable). The construction uses (necessarily) an additional set‐theoretic assumption (the principle) as it was already known, by a result of Fremlin, that it is consistent that such spaces do not exist. This should be compared with the result of Plebanek and Sobota who showed that countable tightness of implies that all Radon measures on have countable type. So, our example shows that the tightness of and of can be different as well as may have Corson property (C), while fails to have it answering a question of Pol. Our construction is also a relevant example in the general context of injective tensor products of Banach spaces complementing recent results of Avilés, Martínez‐Cervantes, Rodríguez, and Rueda Zoca.