Measure Theoretic Probability
Links to notes
Video 3 - How to Use These Videos
Video 4 - Motivation for Measure Theory in Probability Theory
Video 5 - History of Measure Theory - The Source of Our Misery
Video 5.1 - History of Measure Theory - Vitali’s Impossibility
Video 5.2 - History of Measure Theory - Principled Compromise
Video 6 - Canonical Examples of Measures
Video 7.1 - Algebras - Small Examples and a Simple Theorem
Video 8.1 - \(\sigma\)-algebras - Some Algebras Aren’t \(\sigma\)
Video 9 - Generated \(\sigma\)-algebras
Video 9.1 - Generated \(\sigma\)-algebras - Examples
Video 9.2 - Generated \(\sigma\)-algebras - Intersection over Containing \(\sigma\)-algebras
Video 11 - Borel sets
Video 11.1 - Borel sets - Equivalent Basis
Video 12 - Measures
Video 13 - Length-measure
Video 13.1 - Length-measure - \(\mathcal L\) Is a \(\sigma\)-algebra
Video 13.2 - Length-measure - Sub-additivity and Monotonicity
Video 13.3 - Length-measure - Closure under Countable Union
Video 13.4 - Length-measure - m Is a Measure
Video 13.5 - Length-measure - Countable Additivity
Video 13.6 - Length-measure - m Assigns Intervals to Length (1)
Video 13.7 - Length-measure - Countable Implies Null
Video 13.8 - Length-measure - Null Implies Measurable
Video 13.9 - Length-measure - m Assigns Intervals to Length (2)
Video 13.10 - Length-measure - Translation Invariance
Video 13.11 - Length-measure - \(\mathcal B(\Bbb R)\subset \mathcal L\subset \mathcal P(\Bbb R)\)
Video 14 - Generalizing Length-measure
Video 15 - Pre-measures and Semi-algebras
Video 16 - Over-estimates and Outer-measure
Video 17 - The Caratheodory Extension
Video 18 - The Induced Measure Is a Measure of the Semi-algebra
Video 19 - Littlewood’s Three Principles
Video 20 - Measurable Sets Are almost Bases
Video 21 - Outer Regularity
Video 22 - Uniqueness
Video 23 -