Taut Foliations and ℝ‐Covered Foliations With Transverse Measure on 3‐Manifolds

In this paper, we establish a theorem that provides sufficient conditions for a taut foliation on closed 3‐manifolds to be, up to monotone equivalence, a perturbation of a fibration. We also give some conditions under which a taut foliation is ℝ‐covered.