Putting the following three statements together: (a) Assuming that the continuum hypothesis is false, the power of the continuum 2[itex]\aleph0[/itex] is real-valued measurable. (b) The existence of a real-valued measurable and the existence of a measurable (= real-valued measurable & inaccessible) cardinal are equiconsistent. (c) If there exists a measurable cardinal, the continuum hypothesis is false. it sounds like this would imply the following absurd statement: (d) Assuming that the continuum hypothesis is false, the existence of 2[itex]\aleph0[/itex] and the existence of a measurable cardinal are equiconsistent. What is wrong? Is (a) incorrect, or am I putting these together wrong? If (a) is incorrect, is there a clear example to show why?