{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

history-page39

# history-page39 - σ is negligible ◦ Lebesgue ⋆ A set...

This preview shows page 1. Sign up to view the full content.

Characterizations of Riemann-integrability Riemann The norm of a partition is the width of its largest subinterval. A function f is integrable if and only if, for any σ > 0 no matter how small, we can find a norm so that, for all partitions of [a, b] having a norm that small or smaller, the total length of the subintervals where the function oscillates more than
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: σ is negligible. ◦ Lebesgue ⋆ A set has measure zero if it “can be enclosed in a Fnite or a denumerable inFnitude of intervals whose total length is as small as we wish”. Examples of sets of measure zero are N and Q . ⋆ A bounded function is integrable if and only if the set of its points of discontinuity has measure zero....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online