On Baire Property of Spaces of Measurable Functions
DOI:
https://doi.org/10.58649/9scwc676Keywords:
Baire property, function space, measurable functionAbstract
A Tychonoff space X is called a Baire space if the intersection of any countable family of dense open sets in X is again dense in X. One interesting problem in the theory of function spaces is to study when such a function space becomes a Baire space, particularly, in terms of the support of functions considered.
In this paper, it is shown that M(X, K) of all measurable K-valued functions defined on a measurable space (X, Σ) is a Baire space if K is a compact metric space and M(X, K) is equipped with the topology of pointwise convergence.
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