Have studies shown conclusively that the radiation from a lifetime of mammograms does not cause breast cancer? which studies are they?

Probably some risk: The question is whether finding cancers earlier justifies the expense, inconvenience, the trouble and cost of false-positive readings, and perhaps increased cancer risk. There are some good reads bmj. 345:e5660, 2012 suggested for women with brca1/brca2 mutations early mammographs much increase total risk; health physics. 101(5):578-82, 2011 nov. Felt risk is minimal if started in older women.

No,: that type of study would be impossible to perform. Radiation induced cancer risks are extrapolated from various data sources, but not controlled studies. The theoretical slight cancer risk of mammography is dwarfed by the number of cancers mammography detects. You can easily calculate the risks using an interactive tool at xrayrisk.com