Macroeconomics Exam Review 79

Macroeconomics Exam Review 79 - 2.94 We have previously...

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Unformatted text preview: 2.94 We have previously shown that is increasing (Exercise 2.42). By direct calcula- tion, for any constant , ( + )( ) = sup ( ) { ( , ) + ( ( ) + ) } = sup ( ) { ( , ) + ( ) } + = ( )( ) + 2.95 Assume that is a compact subset of ( ). Then is bounded (Proposition 1.1). To show that is equicontinuous, choose > 0. is totally bounded (Exercise 1.113), so that there exist finite set of functions { 1 , 2 ,..., } in F such that min =1 / 3 Each is uniformly continuous (Exercise 2.91), so that there exists > 0 such that ( , ) = ( ( ) , ( ) < / 3 Let = min { 1 , 2 ,..., } . Given any , let be such that...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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