This paper extends a recent investigation of the string theory landscape (Ceresole et al 2006 Phys. Rev. D 74 086010), where it was found that the decay rate of de Sitter(dS) vacua to a collapsing space with a negative vacuum energy can be quitelarge. The parts of space that experience a decay to a collapsing space, or to aMinkowski vacuum, never return back to dS space. The channels of irreversible vacuumdecay serve as sinks for the probability flow. The existence of such sinks is adistinguishing feature of the string theory landscape. We describe relations betweenseveral different probability measures for eternal inflation taking into account theexistence of the sinks. The local (comoving) description of the inflationary multiversesuffers from the so-called Boltzmann brain (BB) problem unless the probability ofthe decay to the sinks is sufficiently large. We show that some versions of theglobal (volume-weighted) description do not have this problem even if one ignoresthe existence of the sinks. We argue that if the number of different vacua in thelandscape is large enough, the anthropic solution of the cosmological constantproblem in the string landscape scenario should be valid for a broad class of theprobability measures which solve the BB problem. If this is correct, the solution of thecosmological constant problem may be essentially measure-independent. Finally, wedescribe a simplified approach to the calculations of anthropic probabilities in thelandscape, which is less ambitious but also less ambiguous than other methods.