Ba space
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- The correct title of this article is ba space. The initial letter is shown capitalized due to technical restrictions.
In mathematics, the ba space ba(Σ) of a sigma-algebra Σ is the Banach space consisting of all bounded and finitely additive measures on Σ. The norm is defined as the variation, that is 
The space ca(Σ) is defined as the subset of ba(Σ) consisting of sigma-additive measures.
[edit] Properties
Both spaces are complete, and thus ca(Σ) is a closed subset of ba(Σ).
The space of simple functions on Σ is dense in ba(Σ).
When Σ is the power set of the natural numbers, ba(Σ) is denoted as ba; it is isomorphic to the dual space of the l-infinity space.
