This paper extends a stability estimate of the Sobolev Inequality established by Bianchi and Egnell in [3]. Bianchi and Egnell's Stability Estimate answers the question raised by H. Brezis and E. H. Lieb in [5]: "Is there a natural way to bound ∇ϕ 2 2 − C 2 N ϕ 2 2N N −2 from below in terms of the 'distance' of ϕ from the manifold of optimizers in the Sobolev Inequality?" Establishing stability estimates -also known as quantitative versions of sharp inequalities -of other forms of the Sobolev Inequality, as well as other inequalities, is an active topic. See [9], [11], and [12], for stability estimates involving Sobolev inequalities and [6], [11], and [14] for stability estimates on other inequalities. In this paper, we extend Bianchi and Egnell's Stability Estimate to a Sobolev Inequality for "continuous dimensions." Bakry, Gentil, and Ledoux have recently proved a sharp extension of the Sobolev Inequality for functions on R + × R n , which can be considered as an extension to "continuous dimensions." V. H. Nguyen determined all cases of equality. The present paper extends the Bianchi-Egnell stability analysis for the Sobolev Inequality to this "continuous dimensional" generalization. * Work partially supported by U.S. National Science Foundation grants DMS 1201354 and DMS 1501007 2 , where β < 2.Recently, Bakry, Gentil, and Ledoux proved a sharp extension of the Sobolev inequality to "fractional dimensions," and showed how it relates to certain optimal Gagliardo-Nirenberg inequalities. V. H. Nguyen has determined all of the extremals in the version of the inequality for real-valued functions. The goal of the present paper is to prove an analogue of Theorem 1.2 for this extended Sobolev inequality. Actually, the case we treat is more general, because we generalize Nguyen's classification of extremals from real-valued functions to complex-valued functions. We then prove the analogue of Theorem 1.2 for this generalization of Bakry, Gentil, and Ledoux's Theorem with classification of extremals for complex-valued functions. This is notable, because Bianchi and Egnell prove their stability estimate for real-valued functions only, while our stability estimate is for complex-valued functions. This is one of the aspects that make our proof more intricate than Bianchi and Egnell's, but it is hardly the most notable or the most difficult aspect to deal with. Some of the steps in the proof of our extension of the Bianchi-Egnell Stability Estimate are a fairly direct adaptation of steps in Bianchi and Egnell's proof. Others are not. To help highlight these differences, we outline a proof of Theorem 1.2 based upon the steps of the proof to our extension of the Bianchi-Egnell Stability Estimate. This outline is provided in subsection 1.5. In the outline, we point out where our approach differs from Bianchi and Egnell's, and in particular, which parts require new arguments.