New MT Article Ideas

Here is a list of new article ideas for the Measure Theory Wiki.

Measurable Sets

• Vitali's Theorem and non-existence of a measure on $2^{\mathbb {R} }$
• Borel $\sigma$-algebra and ${\mathcal {B}}_{\mathbb {R} }$
• ${\mathcal {F}}^{\sigma }$ and ${\mathcal {G}}^{\delta }$ sets
• Product $\sigma$ - algebra
• Borel measureable sets vs. Lebesgue measurable sets

Measures

• Caratheodory's Theorem
• Isomorphism of Measure Spaces
• Lebesgue-Stieljes Measures
• Characterization of Finite Borel Measures
• Approximation by Open/Compact Sets
• Cantor set
• Cantor function

Measurable Functions

• Simple functions