Question

f(x),g(x)是D上的函数，证明inf{f(x)+g(x)}>=inf{f(x)}+inf{g(x)}

为什么f(x)+g(x)>=inf{f(x)}+inf{g(x)},就可以得出inf{f(x)+g(x)}>=inf{f(x)}+inf{g(x)}？

Answer 1

就是说 对任意的x，y g(x)<=f(y)
先固定x，有 g(x)<=所有的f(y),有g(x)<=inf f(y)
而对任意x，都有 g(x)<=inf f(y)
有 sup g(x) <= inf f(y)