3 papers
math.FA2024
L-valued integration
Xingni Jiang, Jan Harm van der Walt, Marten Wortel
We develop integration theory for integrating functions taking values into a Dedekind complete unital -algebra with respect to -valued measures. We then…
math.FA2024
Locally solid convergence structures
E. Bilokopytov, J. Conradie, V. G. Troitsky +1
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with lo…
math.FA2024
L-functional analysis
Eder Kikianty, Miek Messerschmidt, Luan Naude +5
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars or $\mathbb…