Measure Theoretic Structure of Distribution Spaces

This thesis develops a measure-theoretic framework for the representa- tion of distributions in mathematical analysis. Focusing on the duals of the spaces of smooth functions, compactly supported smooth functions, and the Schwartz space, we establish necessary and sufficient conditions for distribu- tions to be represented by Radon measures. Structural theorems and topologi- cal characterizations are proven using tools from topology, functional analysis, and measure theory.