The first image is taken from Geometric Theory of Foliations, Book by A. Lins Neto and César Camacho, Chapter 3, Page 53.
The second image is taken from Geometry, Dynamics And Topology Of Foliations: A First Course, Book by Bruno Scárdua and Carlos Arnoldo Morales Rojas, Chapter 3, Page 56.
In the first image, statement $(c)$ in theorem $7$ the condition $\mu \cap \partial \Sigma = \varnothing$ is not assumed while in proposition $3.2$, in the second image, it is to get the same result.
How could this be?
