| 21. | If the type of partition is limited too much, some non-integrable functions may appear to be integrable.
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| 22. | Since the integral of an integrable function on a set of probability 0 is 0, this proves absolute continuity.
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| 23. | In the " Schr�dinger model ", the Heisenberg group acts on the space of square integrable functions.
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| 24. | The possibility that an integral is unbounded must be avoided, hence attention is restricted to square-integrable functions.
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| 25. | The theorem now holds for square integrable functions on G instead of class functions and the subgroup H must be closed.
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| 26. | An integrable function, in Lebesgue's theory, is equivalent to any other which is the same almost everywhere.
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| 27. | Despite their apparent higher generality, locally-integrable functions form a subset of locally integrable functions for every such that.
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| 28. | Despite their apparent higher generality, locally-integrable functions form a subset of locally integrable functions for every such that.
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| 29. | :: ( b ) There is a constant such that for any locally integrable function on, and all balls:
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| 30. | These are precisely the square-integrable functions that arise as boundary values of holomorphic functions in the open unit disk.
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