Private equity firm Thoma Bravo has closed its inaugural European fund at €1.8 billion ($1.9 billion).Thoma Bravo plans to take equity stakes in mid-sized software companies across Europe.The launch of the fund fills a gap left by North American investment firms retreating from Europe.Thoma Bravo's presence in Europe started in 2011 and it has invested around €14 billion across 16 deals in the region.