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I am reading Probability and Measure by Patrick Billingsley, and I am stuck at one example, please help me understanding it.

http://desmond.imageshack.us/Himg201/scaled.php?server=201&filename=30935274.jpg&res=landing [Broken]

Ω=(0,1]

My question is that how come the A^c = (0,a_1]U(a'_1, a_2]U.....U(a'_m-1, a_m]U(a'_m, 1] ?????? because lets say that A= {(0,0.1], (0.2, 0.3], (0.4, 0.5], (0.6, 0.7], (0.8, 1]} then

A^c = Ω - A

A^c = (0, 1] - {(0,0.1], (0.2, 0.3], (0.4, 0.5], (0.6, 0.7], (0.8, 1]}

A^c = ∅ .........an empty set??????????

You can see this example at http://books.google.co.uk/books?id=...q=probability and measure billingsley&f=false

Example no 2.2 (section: Probability Measure), page 21.

Thanks in advance.

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# Measure theory Question - Help

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