If adidas were to conduct a survey to find out what percentage of consumers could identify the "three stripe" logo as belonging to the adidas brand, which aspect of brand equity would they be measuring?

The aspect of brand equity which would be measured when conducting this type of survey is brand association. Logo is another perception of customers for brand name. When customers are aware of the logo of the products they are buying it simply means they are familiar of that brand and associate factors related to it such as quality.