Let a < c < b and let 8' and 8" be gauges on [a, c] and [c, b], respectively. H 8 is
Chapter 5, Problem 6(choose chapter or problem)
Let a < c < b and let 8' and 8" be gauges on [a, c] and [c, b], respectively. H 8 is defined on [a, 6] by I 8' (t) if t e [a, c), 8(t) := min{8'(c), &"(c)} if t = c, 8"(t) if t e (c,b], then 8 is a gauge on [a, b]. Moreover, if P' is a 8' -fine partition of [a, c] and P" is a 8" -fine partition of[c, b], then P' UP" is a tagged partitionof[a, b] having cas a partition point. Explain I II why 'P U 'P may not be 8-fine. Give an example.
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