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