Math 108b
 
Classical Analysis
Winter 2014-15
 
MWF 11:00 AM // 151 Sloan 
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Instructor:  Nets Katz, 266 Sloan, 626-395-2326, nets @ caltech.edu
Office Hours: W 5-6


Lead TA:  Isak Mottleson 379 Sloan imottels@caltech.edu
Office Hours: Thursdays 4-5


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Math 108(b) will be principally concerned with developing the theory of Lebesgue measure. This deals with the fundamental question of how we should think of the size of a set of real numbers. Once we have this under control, we will develop a notion of integration which somewhat generalizes the Riemann integration which is taught in Math 1a. By studying Lebesgue theory in this way, in depth and from the ground up, we will gradually develop and understand some of the powerful techniques of analysis which can be used in almost any situation. In particular, we will study the Dominated convergence theorem and the Lebesgue differentiation theorem. We will discuss some of the far-reaching consequences of the techniques used in proving the Lebesgue differentiation theorem.

Prerequisites:  Math 108a .

 


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Textbook:
Measure and Integral, R.L. Wheeden and A. Zygmund, ISBN: 0824764994
 

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