Search for tag: "analysis"

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 0 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 0 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 0 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 19 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 0 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 27 plays 1  

Advanced Manufacturing Building official opening

With manufacturing on the cusp of a technological revolution, a flagship research facility has opened its doors at the University of Nottingham to help future-proof UK industry in a competitive…

From  Emma Lowry on December 13th, 2018 0 likes 127 plays 0  

Dr Carl Mundy, PhD alumnus talks about using the Careers and Employability Service

Carl talks about how the Careers and Employability Service helped him achieve his career aim. He attended a range of workshops and now on reflection says he should have used them more!

From  Jackie Thompson on April 5th, 2017 0 likes 41 plays 0  

Dr Carl Mundy - PhD Astronomy to Data Analyst

Carl talks about how his interest in writing software during his PhD lead to his interest in data analysis. He also identifies the transferable skills he developed during his PhD, through a work…

From  Jackie Thompson on April 5th, 2017 0 likes 63 plays 0  

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 62 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 0 plays 0  

#askatheologian Why do we need chapters and verses?

Professor Tom O’Loughlin explains that the familiar chapters and verses – found in every printed bible – are to be viewed solely as a means of finding passages and particular…

From  Simon Barnett on January 27th, 2015 0 likes 0 plays 0  

Detectives of Corrosion

Corrosion costs the oil and gas industry billions of dollars every year, it can also have far reaching environmental consequences. But so far no one has managed to stop corrosion happening. Experts…

From  Digital Communications on October 3rd, 2013 0 likes 0 plays 0