# Measure Theory and Integration

Fundamentals of measure and integration theory. Lecture series.

28 Jul 2014 to 25 Sep 2014

What does it mean for a subset *E* of * R^{d}* to be measurable? If a set

*E*is measurable, how does one define its measure? What nice properties or axioms does measure (or the concept of measurability) obey? Does the measure of an “ordinary” set equal the “naive geometric measure” of such sets? (e.g. is the measure of an

*a*×

*b*rectangle equal to

*ab*?)

Trying to answer these questions, we will study the concepts of Jordan measure and Riemann integral which are elementary enough to measure most of the “ordinary” sets (like area under the curve of a continuous function) and then a more general notion of Lebesgue measure and Lebesgue integral which extends the Jordan measure to measure almost all sets that arise in analysis.

Measure theory and integration theory are of fundamental importance in all of applied mathematics, specifically in the foundations of probability theory, and in the theory of differential equations.

**Lecturer:** Tanmay Bichu.

**Venue:** Noumenon Multiphysics.

**List of lectures:**

28 Jul 2014 | Measuring sets with a graph paper |

30 Jul 2014 | Jordan measure |

4 Aug 2014 | Translation invariant sets |

6 Aug 2014 | Translation invariance of Jordan measure |

10 Sept 2014 | Reimann Integral and it's relation with Jordan measure |

12 Sept 2014 | Linearity of Reimann Integral |

17 Sept 2014 | Properties of Reimann Integral & IVT for integrals |

*This lecture series is in progress. If you
wish to attend, or wish to hold a similar lecture series at your venue,
please send an email to training@noumenonmp.com. *

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