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In this chapter we deal with the strong Luzin ((SL)-) integral, related with the existence of primitives of functions in the weak sense. This integral is a variant of the Kurzweil-Henstock integral, which coincides with it in the real case, but is in general slightly different in the context of Riesz spaces, because some pathologies can occur. We also prove some versions of Hake and monotone convergence type theorems and of the Fundamental Theorem of Calculus, together with the basic properties.
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