Here is the AP's fact check of Trump's RNC speech
Briefly

Trump's speech contained false and misleading claims, suggesting a surge in violent crime due to immigration influx. However, FBI stats and studies show lower crime rates among undocumented immigrants compared to native-born Americans.
Contrary to Trump's claims, there is no evidence of increased crime by migrants, either at the U.S.-Mexico border or in cities with high migrant populations. National statistics actually indicate a decrease in violent crime.
Read at Boston.com
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