j*****h
发帖数: 3 | 1 Does there exist a measurable function f:S->R, such that f(x) > 0 for all x
in S, yet the Lebesgue integral of f over S equals 0? S is not a null set.
Thanks! | x*****d
发帖数: 427 | 2 no. S split to a countable union U {f(x)>1/k}
x
【在 j*****h 的大作中提到】
: Does there exist a measurable function f:S->R, such that f(x) > 0 for all x
: in S, yet the Lebesgue integral of f over S equals 0? S is not a null set.
: Thanks!
| j*****h
发帖数: 3 | 3 thx
【在 x*****d 的大作中提到】
: no. S split to a countable union U {f(x)>1/k}
:
: x
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