Channel 4, which has been picking up momentum in recent months, continued to show gains in several day parts during October, according to the Arbitron ratings book issued this week. . .

Helped by the continuing strength of "People's Court" as its Monday-Friday 5 p.m. lead-in to the early news . . . Four, with an eight rating and a 23 percent audience share, is making a real fight of it at 5:30 with Nine (8/24), while Seven registers a 4/13, down a point and four shares from the same period in 1981. . .

WRC, on the other hand, has picked up three ratings points and seven share points from the October 1981 book in that time period (Nine is down a share). . .

From 6 to 7 (Monday-Friday) Nine's "Eyewitness News" is far ahead, with a 12/28 . . . compared with Four's 9/20 and Seven's 7/16 (which represents a gain of 2/3 for WRC over last year in that time period). . .

WRC's best performance is at 11 p.m. (seven nights), coming in first with a 9/27 (compared with 6/19 a year ago). . .

Nine is second at 11 p.m. with an 8/23 (up a rating point from last year), and Seven trails with a 7/19 (down four share points from last year). . .

Keeping firmly in mind that NBC carried the World Series in October . . . WRC's growth in prime time over October 1981 was spectacular. . .

WRC was first in prime time (seven nights a week) with a 16/28 . . . up from 12/23 a year ago. . .

WDVM was second with a 15/26 (down two share points from '81), while WJLA, which carried the Series last year, had a 14/24 . . . down from a 17/33 in '81. . .

WRC even finished in a three-way tie for first with WDVM and WJLA in the sign-on to sign-off (7 a.m. to 1 a.m.) ratings, despite the fact that NBC's daytime schedule is by far the weakest on network television. . .

All three had 6/23 for the broadcast day, which represented drops of 1/4 for both WDVM and WJLA from last year . . . while WRC registered a 1/3 gain over October '81. . .

WTTG was fourth in sign-on to sign-off, with a 4/15, which matched last year's performance, while WDCA, with a 2/6, was down a share point from a year ago in October.