Minorizing measures and truncations of measurable lattice-path matroids

For a measurable lattice-path matroid specified by an arbitrary closed set of constrained times and lower and upper cumulative paths, this manuscript determines both minorizing-measure relaxations exactly. The basic minorizing measures form the weak-star compact fixed-mass path corridor, while all minorizing measures form the interval relaxation forced by the boundary paths. Every real truncation is therefore one total-mass slice of that interval relaxation. For the full-rank basic corridor, the paper also gives the exact contact-set criterion for extreme points and proves that every such extreme point is weak-star exposed. Status: Public Beta v0.1-beta; internally verified candidate proof; external review pending.