(a) Let D denote the set of points
at which the function f is discontinuous. Find D.
(b) Show that a circle in the plane has zero content. (Hint: Use Proposition 4.19(c), which states If f:
is of Class
, then f([a,b]) has zero content whenever
(c) Show that the set D has zero content.
Remark: It follows from part (c) that f is integrable over any measurable region in the plane. See Theorem 4.21, which states the following: Let S be a measurable subset of R^2. Suppose
is bounded and the set of points in S at which f is discontinuous has zero content. Then f is integrable on S.
How would I go about finding the set D for (a)? I know f is a discontinuous function but how would I find the exact (x,y)?