# Reference : Proving something is a Brownian Motion

Given a (standard) Brownian Motion $$W_t$$ if we do some sort of scaling, inversion or reversal then we also get a Brownian motion.

I have seen proofs but the proofs only seem to rely on showing covariance is the minimum of two given (arbitrary) times and the continuity.

I can't seem to find a theorem or lemma in my book that states this is all that needs to be checked rather than entirely check the 4 parts of the definition of Brownian motion.

Could someone either state or give reference (which I can find online) to this? That is much simpler than having to prove by the definition.