Topic: The Riesz Representation Theorem

Properties of the Open-Set Content

Positive Linear Functionals on C_c(X)

Open-Set Contents Induced by a Functional

Locally Compact Hausdorff Spaces and C_c(X)

Local Finiteness and Regularity of the Constructed Measure

Integrating Continuous Functions Against Radon Measures

Functional Norm and Total Mass

Constructing an Outer Measure from Open Covers

Choosing C_c, C_0, and C(X) Correctly

Caratheodory Measurability of Borel Sets