Many of the properties of te Lebesgue measure as stated on this page are simply properties of measures in general. Items 3 and 4 for example, and perhaps others (I don't know, since I'm just learning about the subject as I browse here!)
Wouldn't it be better to list only those properties that are specific to the Lebesgue measure, or at least to indicate which ones are? The standard definition is already there at measure
Also, a measure is defined on its page as a function on a sigma algebra; if that's really part of the definition, then saying "the Lebesgue measurable sets therefore form a sigma algebra" seems a little redundant and/or confusing.
Is it clearer now? --AxelBoldt
Thanks. I'm still a little unsure as to which properties listed are common to all measures, and which are special to Lebesgue measure, but that's mainly due to my near-total ignorance of the whole subject. - Stuart