APPLIED GENERAL TOPOLOGY, cilt.16, sa.2, ss.167-181, 2015 (ESCI)
This is a continuation of the work where the notions of Lebesgue uniformity and Lebesgue quasi uniformity in a texture space were introduced. It is well known that the quasi uniform space with a compact topology has the Lebesgue property. This result is extended to direlational quasi uniformities and dual dicovering quasi uniformities. Additionally we discuss the completeness of lebesgue di-uniformities and dual dicovering lebesgue di-uniformities.