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8
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Let f be a function defined on an interval Δ which may be (un)bounded. Then f is uniformly continuous on Δ if
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It is continuous at every point to every other point
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10
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11
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If f is lipschtiz continuous on Δ
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Which then also implies that it is continuous on Δ
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13
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And example
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17
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Disprove!
Find a single point (finite or infinite) where f is not uniformly continuous
Look for a point where f oscillates or grows
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19
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Boundedness theorem
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If f is a continuous function on a closed bounded interval, then f is bounded
20
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How to prove that if f is Lipshcitz continuous on Δ then f is uniformly continuous on Δ
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Take δ_ε = ε/C in definition of uniform continuity
KCL Real Analysis
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Decks in class (11)
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