- January 2016
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- An order-based integration of scalar functions with respect to positive vector measures with values in quasi-Banach lattices is presented. It is proved that it coincides with the Bartle-Dunford-Schwartz-type integration for the case of positive measures. These ideas are used to obtain general representation theorems for abstract order continuous quasi-Banach lattices with weak unit without any previous representation of these spaces as spaces of integrable functions. In the case of quasi-Banach lattices having some convexity, it is shown that this representation can be improved.
- quasi-banach lattice; vector-valued integration; representation theorem; spaces; operators