- #1
chipotleaway
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Why is the characteristic function* of a ball in Rn continuous everywhere except on its surface?My lecturer said that a circle is a 'set of discontinuities' - what exactly does that mean?
(some context: we're looking at how we can integrate over a ball. Previously we've only looked at Riemann integration over rectangles - for that, he also introduced the theory by first defining integrals for the characteristic function over rectangles).
*The characteristic function of any set in Rn was defined to be 1 if x was a point inside the set and 0 if t was outside
(some context: we're looking at how we can integrate over a ball. Previously we've only looked at Riemann integration over rectangles - for that, he also introduced the theory by first defining integrals for the characteristic function over rectangles).
*The characteristic function of any set in Rn was defined to be 1 if x was a point inside the set and 0 if t was outside