Search for tag: "theory"

Measure Theory (11/15) - Properties of measures (1/2)

Deduction of standard properties of measures from the two axioms: finite additivity; monotonicity; countable subadditivity. Continuity properties of measures stated and discussed. For more…

From  Joel Feinstein on April 12th, 2020 0 likes 10 plays 0  

Measure Theory (10/15) - Measurable spaces, measurable sets, measures and measure spaces (2/2)

Terminology: countable additivity, pairwise disjoint unions. Notation for pairwise disjoint unions. Examples and constructions of measures: counting measure; combinations of measures; the biggest…

From  Joel Feinstein on April 12th, 2020 0 likes 13 plays 0  

Measure Theory (9/15) - Measurable spaces, measurable sets, measures and measure spaces (1/2)

Measurable spaces and measurable sets. Brief discussion of length, area and volume, the idea behind Lebesgue measure, and some of the issues. The definition of a (non-negative) measure on a…

From  Joel Feinstein on April 12th, 2020 0 likes 18 plays 0  

Measure Theory (8/15) - The sigma-algebra generated by a collection of subsets (2/2)

Properties of the sigma-algebra on a set X generated by a collection of subsets. Methods for showing inclusion or equality of sigma-algebras generated by two different collections of subsets. The…

From  Joel Feinstein on April 12th, 2020 0 likes 19 plays 1  

Measure Theory (5/15) - Collections of sets (1/2)

Sets of sets, which we call collections of sets.Comparison of the properties of some collections of sets, including topologies, and the collection of closed sets in a topological space.Definition, …

From  Joel Feinstein on April 9th, 2020 0 likes 17 plays 1  

Measure Theory (4/15) - The algebra of limits

The algebra of limits for sums of sequences of non-negative extended real numbers. The algebra of limits for products, and its limitations, for sequences of non-negative extended real numbers. For…

From  Joel Feinstein on April 9th, 2020 0 likes 12 plays 0  

Measure Theory (3/15) - Arithmetic and series in the non-negative extended real numbers

Addition and multiplication for non-negative extended real numbers. Problems with the cancellation laws. Series of non-negative extended real numbers. Some discussion of problems with the algebra of…

From  Joel Feinstein on April 9th, 2020 0 likes 17 plays 0  

Measure Theory (2/15) - The extended real line (2/2)

Discussion of convergence to infinity for sequences of non-negative extended real numbers. Monotone sequences (nondecreasing or nonincreasing) and the Monotone Sequence Theorem for the extended real…

From  Joel Feinstein on April 9th, 2020 0 likes 16 plays 0  

Measure Theory (1/15) - The extended real line (1/2)

An introduction to the extended real line, with its total order (extending the total order on the real line), and a metric (induced, via a suitable bijection, by the usual metric on [-1,1]). Brief…

From  Joel Feinstein on April 9th, 2020 0 likes 24 plays 1  

Measure Theory (7/15) - The sigma-algebra generated by a collection of subsets (1/2)

Audio narration (with digital pointer) to go with Slide 37 of G14FTA where the original recording failed. Brief discussion of how to generate a topology from a collection of sets (as a sub-base), and…

From  Joel Feinstein on February 22nd, 2017 0 likes 61 plays 0  

Measure Theory (6/15) - Collections of sets (2/2)

Audio narration (with digital pointer) to go with the annotations of slides 35-36 from G14FTA Further Topics in Analysis, where the original recording failed. More examples of σ-algebras:…

From  Joel Feinstein on February 22nd, 2017 0 likes 45 plays 0  

M12101 Social and Global Justice

M12101 Social and Global Justice with David Stevens

From  John Pollock on March 31st, 2015 0 likes 809 plays 0  

M13211 The Rights and Wrongs of Climate Change

M13211 The Rights and Wrongs of Climate Change with Matthew Rendall

From  John Pollock on March 9th, 2015 0 likes 430 plays 0  

M13107 Feminist Political Theory

M13107 Feminist Political Theory with Lucy Sargisson

From  John Pollock on March 9th, 2015 0 likes 125 plays 0