- Littlewood's three principles of real analysis
**Littlewood's three principles of**arereal analysis heuristics ofJ. E. Littlewood to help teach the essentials ofmeasure theory inmathematical analysis .**The principles**Littlewood stated the principles in his 1944 "Lectures on the Theory of Functions" [

*cite book*] Rp|26as:

last=Littlewood

first=J. E.

authorlink=John Edensor Littlewood

title=Lectures on the Theory of Functions

year=1944

publisher=Oxford University Press

oclc=297140The first principle is based on the fact that the

inner measure andouter measure are equal for measurable sets, the second is based onLusin's theorem , and the third is based onEgorov's theorem .**Example**Littlewood's three principles are quoted in several real analysis texts, for example Royden,cite book

last = Royden

first = H. L.

title = Real Analysis

publisher = Macmillan

location = New York

edition=3rd edition

year = 1988

isbn = 9780024041517 ] Rp|72Bressoud, [] Rp|191and Stein & Shakarchi. [*cite book*] Rp|33Unfortunately most authors quote the principles to point out which theorems are the most important, not as a heuristic.

last = Stein

first = Elias

authorlink = Elias M. Stein

coauthors = Rami Shakarchi

title = Real Analysis: Measure Theory, Integration, and Hilbert Spaces

url = http://press.princeton.edu/chapters/s8008.pdf

format = PDF

accessdate = 2008-07-03

publisher = Princeton University Press

location = Princeton

year = 2005

isbn = 9780691113869**Notes**

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