Measure Theoretic Probability 1 1Y4XD290EH
| URI | m2://res/1Y4XD290EH |
|---|---|
| Kind | course |
| Creators | Suprio Bhar (instructor) |
| Date | 2021-07-25 |
| Scope | in |
| Ids | course 05pjsgx75:111104152 |
Expressions
e1: edition
| Language | en |
|---|---|
| Date | 2021-07-25 |
- m1: page, IIT Kanpur (record). nptel 111104152
- m2: page, 2021-07-25 (record). nptel 111104152
Contents
- part 1: Week 1: Random Experiments and Sigma-fields
- session 1: Lecture 01: Introduction to the course Measure Theoretic Probability 1
- session 2: Lecture 02: Sigma-fields and Measurable spaces
- session 3: Lecture 03: Fields and Generating sets for Sigma-fields
- session 4: Lecture 04: Borel Sigma-field on R and other sets
- session 5: Lecture 05: Limits of sequences of sets and Monotone classes
- part 2: Week 2: Measures and Measure Spaces
- session 6: Lecture 06: Measures and Measure Spaces
- session 7: Lecture 07: Probability Measures
- session 8: Lecture 08: Properties of Measures (Part 1)
- session 9: Lecture 09: Properties of Measures (Part 2)
- session 10: Lecture 10: Properties of Measures (Part 3)
- part 3: Week 3: Borel Measurable Functions and Random Variables
- session 11: Lecture 11: Measurable functions
- session 12: Lecture 12: Borel measurable functions
- session 13: Lecture 13: Algebraic properties of Measurable functions
- session 14: Lecture 14: Limiting behaviour of measurable functions
- session 15: Lecture 15: Random Variables and Random Vectors
- part 4: Week 4: Law and Distribution Function of a random variable
- session 16: Lecture 16: Law or Distribution of an RV
- session 17: Lecture 17: Distribution Function of an RV
- session 18: Lecture 18: Decomposition of Distribution functions
- session 19: Lecture 19: Construction of RVs with a specified law
- session 20: Lecture 20: Caratheodery Extension Theorem
- part 5: Week 5: Correspondence between Distribution functions and Probability measures
- session 21: Lecture 21: From Distribution Functions to Probability Measures (Part 1)
- session 22: Lecture 22: From Distribution Functions to Probability Measures (Part 2)
- session 23: Lecture 23: Lebesgue-Stieltjes Measures
- session 24: Lecture 24: Properties of Lebesgue Measure on R
- session 25: Lecture 25: Distribution Functions and Probability Measures in higher dimensions
- part 6: Week 6: Expectation of a discrete RV
- session 26: Lecture 26: Integration of measurable functions
- session 27: Lecture 27: Properties of Measure Theoretic Integration (Part 1)
- session 28: Lecture 28: Properties of Measure Theoretic Integration (Part 2)
- session 29: Lecture 29: Monotone Convergence Theorem
- session 30: Lecture 30: Computation of Expectation for Discrete RVs
- part 7: Week 7: Convergence Theorems involving Expectations of RVs
- session 31: Lecture 31: MCT and the Linearity of Measure Theoretic Integration
- session 32: Lecture 32: Sets of measure zero and Measure Theoretic Integration
- session 33: Lecture 33: Fatou's Lemma and Dominated Convergence Theorem
- session 34: Lecture 34: Riemann and Lebesgue integration
- session 35: Lecture 35: Computations involving Lebesgue Integration
- part 8: Week 8: Expectation of an Absolutely Continuous RV
- session 36: Lecture 36: Decomposition of Measures
- session 37: Lecture 37: Absolutely Continuous RVs
- session 38: Lecture 38: Expectation of Absolutely Continuous RVs
- session 39: Lecture 39: Inequalities involving moments of RVs
- session 40: Lecture 40: Conclusion to the course Measure Theoretic Probability 1
Catalogue records
- nptel: 111104152 (manifestation)
- nptel_video: 111104152 (manifestation)