continuous functions are measurable

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Example

f:R→R continuous ⟹ f is measurable
Notice that for all α∈R, we have

f−1((α,∞])=f−1((α,∞))

is the preimage of an open set. And because f is continuous, this preimage is also open and therefore measurable.

This follows immediately from the inverse image of measurable functions of all borel sets are measurable.

References

References

See Also

Mentions

Mentions

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