The network finished the quarter that ended in June first in total prime-time viewers and first among those 25 to 54 years old, growing 21% in that key demographic compared with the year-earlier period, according to Nielsen. Mr. Carlson has proved a solid replacement for Mr. O’Reilly, at lower cost, and the round-table show “The Five” is up slightly in the ratings over Megyn Kelly’s “The Kelly File.” Ms. Kelly left for NBC early this year…

Still, the landscape has shifted. Ratings for all three cable networks are up substantially from before the presidential election cycle, but MSNBC is enjoying the most sustained growth, with liberal audiences hungry for a critical point of view on the Trump administration. Its viewership among those 25 to 54 grew 72% year-over-year in the quarter that ended in June, narrowing the gap with Fox News considerably. MSNBC’s Rachel Maddow’s show is No. 1 overall on cable in total viewers and in the key demographic.