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

Rok, strany: 2014, 727 - 740

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 $\mathcal A$ of subsets of $X$. Secondly, instead of the length of intervals ($\lambda([c,d])=d-c$) any vector measure $\lambda\:\mathcal A \to V$ is considered, where $V$ is a Riesz space.

ISO 690:

Riečan, B. 2014. On the Kluvánek construction of the Lebesgue integral with respect to a vector measure. In Mathematica Slovaca, vol. 64, no.3, pp. 727-740. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0236-4

APA:

Riečan, B. (2014). On the Kluvánek construction of the Lebesgue integral with respect to a vector measure. Mathematica Slovaca, 64(3), 727-740. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0236-4