Constructions and Properties of Quasi Sigma-Algebra in Topological Measure Space

The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in Hausdorff based on locally compactable neighborhood systems without considering strictly (metrized) Borel variety. null extension gives rise to quasi sigma-semiring sigma-neighborhoods, which are rectifiable view Dieudonné n-space. concepts symmetric signed measure, uniformly pushforward and its interval-valued Lebesgue variety within introduced. preserves total ordering real line; however, collapse symmetry admits space. constant measures compact supports sigma-neighborhood invariant under deformation retraction simply connected where sequence retractions induces strongly convergent measures. Moreover, sigma-structures an automorphic isomorphic preserve properties measure. Haar-measurable group structures equivalent additive integer groups arise as long non-compact null-extended system groups. comparative analyses proposed with respect existing results outlined.