Order-type Henstock and McShane integrals in Banach lattice setting

Abstract

We study Henstock-type integrals for functions defined in a compact metric space $T$ endowed with a regular $\sigma$-additive measure $\mu$, and taking values in a Banach lattice $X$. In particular, the space $[0,1]$ with the usual Lebesgue measure is considered.

5 pages

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• Filter convergence and decompositions for vector lattice-valued measures
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• Kuelbs-Steadman spaces for Banach space-valued measures
• A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability
• Set-valued Brownian motion
• A Girsanov Result through Birkhoff Integral