currently i'm studynig "Introduction to dyamical systems" By stuck and Brin. In chapter 6 they define absolutely continuous and transversely absolutely continuous foliations. By prposition 6.2.2 If $W$ is transversely absolutely continuous then it is absolutely continuous.But the coverse is not true in general.

  I'm looking for an example of an absolutely continuous foliation, which is not transversely absolutely continuous.

Thanks.

Currently I'm studying "Introduction to dyamical systems" by Stuck and Brin. In chapter 6 they define absolutely continuous and transversely absolutely continuous foliations. By proposition 6.2.2 if $W$ is transversely absolutely continuous then it is absolutely continuous. But the converse is not true in general. I'm looking for an example of an absolutely continuous foliation which is not transversely absolutely continuous.