Embedded spaces of Haar type on arbitrary irregular grids are discussed. The mentioned spaces are selected adaptively depending on the initial numerical flow. To expand the criteria for adaptability, two types of pseudo-measure are introduced. One type of pseudo-measure is defined on the segments of the real axis, and the other type is set on the subsets of the initial grid. Introduced concepts are used to construct embedded the Haar spaces with adaptivity properties in the norms of the spaces C. The approximate properties are determined by constructed spaces. The computational complexity of the obtained algorithm is investigated. The complexity is directly proportional to the length of the initial number flow.