25 citations · 31 across the 2 of their papers we have counts for
4 papers
Hausdorff Compactifications
Matt Insall, Peter A. Loeb, Malgorzata Aneta Marciniak
Previously, the authors used the insights of Robinson's non-standard analysis as a powerful tool to extend and simplify the construction of some compactifications of regular spaces…
An Intuitive Approach to the Martin Boundary
Peter A. Loeb
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic fun…
Lusin's Theorem and Bochner Integration
Peter A. Loeb, Erik Talvila
It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover,…
Covering theorems and Lebesgue integration
Peter A. Loeb, Erik Talvila
This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let be a finite dimensional no…