A charge space ( X , 𝒜, µ ) is a generalisation of a measure space, consisting of a sample space X , a field of subsets 𝒜 and a finitely additive measure µ , also known as a charge . Properties a real-valued function on X may possess include T 1 -measurability and integrability. However, these properties are less well studied than their measure-theoretic counterparts. This paper describes new characterisations of T 1 -measurability and integrability for a bounded charge space ( µ ( X ) < ∞). These characterisations are convenient for analytic purposes; for example, they facilitate simple proofs that T 1 -measurability is equivalent to conventional measurability and integrability is equivalent to Lebesgue integrability, if ( X , 𝒜, µ ) is a complete measure space. New characterisations of equality almost everywhere of two real-valued functions on a bounded charge space are provided. Necessary and sufficient conditions for the function space L 1 ( X , 𝒜, µ ) to be a Banach space are determined. Lastly, the concept of completion of a measure space is generalised for charge spaces, and it is shown that under certain conditions, completion of a charge space adds no new equivalence classes to the quotient space ℒ p ( X , 𝒜, µ ).