Alphabeta MathStandard-Borel Real Codings and Determining Classes: Examples
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1 · Prerequisites
Measure Theory
Probability
Real Analysis
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Countability and Uncountability
- Foundations of the Real Numbers for Analysis
- Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Series: Convergence and the Nonnegative Tests
- Suprema and Infima
- The Cantor Set, Baire Category, and Measure Zero in ℝ
- Topology of ℝ
Set Theory
Topology
- Compactness
- Compactness in Metric Spaces
- Complete Metrizability, Čech-Completeness, and Baire Category
- Completeness, Completion, and Uniform Continuity
- Countability Axioms and Cardinal Functions
- Metric Spaces
- Separation Axioms: the Hierarchy
- Subspaces, Products, and Quotients
- Topological Spaces and Continuity
2 · Logical flowchart
3 · Items
Example
Countable discrete spaces are standard borel
Example
Euclidean borel spaces are standard borel
Example