Interactive Real Analysis
- part of Proposition 7.4.15: Measurable Functions are Almost Continuous
Suppose f is a measurable function defined on an interval
[a, b] such that the set where f is plus or minus
infinity has measure zero. Then, for any 
> 0
we can find a step function g and a continuous function h
such that
.
Context
> 0
we can find a step function g and a continuous function h
such that
| f(x) - g(x) | <except on a set of measure less than
| f(x) - h(x) | <
.
Context