Bounded Linear Functionals on Ｃ[0, 1]

• Main Authors: Ou-Yang Pei, 歐陽霈
• Other Authors: Tzeng Shyuh-yaur
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/55382601437411728406

碩士 === 國立彰化師範大學 === 數學系所 === 99 === Given a continuous linear functional(equation),we want to seek a function(equation)of bounded variation on(equation)such that(equation)for all(equation).And this proof has two case: The first is that(equation),and the second is that(equation)is a general functional. For the first case, we define a function(equation),and proving something, and finally, define a function(equation),we can seek a function(equation)of bounded variation such that(equation).For the second case, first we define a function(equation), and proving something, and define a function(equation), and proving something, and finally, by Helly’s Theorem, and define a function(equation),we can seek a function(equation)of bounded variation such that(equation).