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We give two new versions of the LS category for the set-up of measurablelaminations defined by Berm\'udez. Both of these versions must be considered as"tangential categories". The first one, simply called (LS) category, is thedirect analogue for measurable laminations of the tangential category of(topological) laminations introduced by Colman Vale and Mac\'ias Virg\'os. Forthe measurable lamination that underlies any lamination, our measurabletangential category is a lower bound of the tangential category. The secondversion, called the measured category, depends on the choice of a transverseinvariant measure. We show that both of these "tangential categories" satisfyappropriate versions of some well known properties of the classical category:the homotopy invariance, a dimensional upper bound, a cohomological lower bound(cup length), and an upper bound given by the critical points of a smoothfunction.

Measurable versions of the LS category on laminations