Before revision:  In the spirit of the Fundamental Theorem of Asset Pricing (FTAP) , it is shown that there is  absence of arbitrages of the first kind in the market if and only if an equivalent local martingale deflator (ELMD) exists. An ELMD is a strictly positive process that , when deflated by it, discounted nonnegative wealth processes become local martingales.
After revision:  In the spirit of the Fundamental Theorem of Asset Pricing (FTAP) , it is shown that there is absence of arbitrages of the first kind and the existence of a strictly positive process that , when deflated by it, discounted nonnegative wealth processes become local martingales.