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On the Kluvánek construction of the Lebesgue integral with respect to a vector measure

The Kluvánek construction of the Lebesgue integral is extended in two directions. First, instead of a compact interval [a, b] in the real line an abstract non-empty set X is considered, instead of the ring generated by subintervals of [a, b] an arbitrary ring A of subsets of X. Secondly, instead of the length of intervals (λ([c, d]) = d−c) any vector measure λ: A→V is considered, where V is a Riesz space.