Re: Concept of measure in undergraduate mathematics.

From: Timothy Murphy (tim_at_birdsnest.maths.tcd.ie)
Date: 03/23/05 

Date: Wed, 23 Mar 2005 12:39:53 +0000

Herman Rubin wrote:

>>Another question: if the preferred manner of introducing Lebesgue
>>integration is via the area under the graph of a step function (in the
>>style of Weir's Lebesgue Integration and Measure, for example) could
>>such an approach be used in something like the above scheme?
>
> This is done too often. Lebesgue's original approach to
> integration was better.

I don't agree.
The idea of area is freely used in secondary and even primary education,
long before it can be rigorously justified
(rather like the Fundamental Theorem of Arithmetic)
and it seems to me that one of the first tasks of a university maths course
should be to shore up the basic idea of area (and volume). 

-- 
Timothy Murphy  
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland

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