The statement is no longer true when the boundedness condition is relaxed to even .[2]
Notes
^Dunford, Nelson; Schwartz, J. T. (1956), "Convergence almost everywhere of operator averages", Journal of Rational Mechanics and Analysis, 5: 129–178,
MR0077090.
^Friedman, N. (1966), "On the Dunford–Schwartz theorem", Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 5 (3): 226–231,
doi:10.1007/BF00533059,
MR0220900,
S2CID122257150.
The statement is no longer true when the boundedness condition is relaxed to even .[2]
Notes
^Dunford, Nelson; Schwartz, J. T. (1956), "Convergence almost everywhere of operator averages", Journal of Rational Mechanics and Analysis, 5: 129–178,
MR0077090.
^Friedman, N. (1966), "On the Dunford–Schwartz theorem", Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 5 (3): 226–231,
doi:10.1007/BF00533059,
MR0220900,
S2CID122257150.