5:35 PM PT -- Vanessa is thanking the "millions of people who've shown support and love during this horrific time." She just posted a heartwrenchingly beautiful family photo of Kobe, herself an their 4 daughters.
Vanessa says they are "completely devastated by the sudden loss of my adoring husband, Kobe -- the amazing father of our children; and my beautiful, sweet Gianna." She also says they're struggling to imagine life without them, but adds ... "we wake up each day, trying to keep pushing because Kobe, and our baby girl, Gigi, are shining on us to light the way.