Lebesgue and co-Lebesgue di-uniform texture spaces

The author introduces the notions of Lebesgue di-uniformity and co Lebesgue di-uniformity and investigates the relationship between a Lebesgue quasi uniformity on X and the corresponding Lebesgue di-uniformity on the discrete texture ( X , P ( X ) ) . Finally a notion of a dual dicovering Lebesgue quasi di-uniform texture space is introduced and several properties are discussed.