Options for ridding records of static electricity

Thanx Antin, very helpful. I would just like to make several comments in addition. The charge is developed during play. Devices that neutralize the static before play are not useful. The charge develops rapidly and spreads over the surface of the record. The record collects dust during play especially if you are not using a dust cover. You can charge the record by rubbing your hand back and forth across the record, a behavior most of us would cringe to think about. Grounding the platter does not work. Even if you discharged the bottom of the record you are not discharging the top of the record. Static does not make a U turn around a sharp edge.  Also very few mats are conductive. Many platters now are not conductive
You mention conductive brushes and why  handheld brushes do not work. Good conductive sweep arms use the same bristles used in the hand held brushes just a bit longer. The arm I currently use, this one 
https://www.sleevecityusa.com/Antistatic-Record-Cleaning-Arm-p/tac-01.htm  is quite durable. Mine must be 6 years old at least and shows no sign of giving up. It is admittedly a little flimsy is some ways but with slight modification it stays permanently in adjustment and is a breeze to use.
The arm is set up so that the bristles just barely touch the record. This gives the best tracking and clears any incidental dust away from the stylus. I have a felt pad stuck to the left front corner of the turntable which I wipe the brush on before play. I clean the pad every so often with alcohol. I clean the arm maybe twice yearly with alcohol. The arm works perfectly. You can not hear it tracking the record. You can not hear it through the system even if you drop it on the record during a silent groove. If you use the right sleeves the records never hold any static charge, not even a whisper and the records remain perfectly clean. If you do not use a dust cover during play the records won't remain quite as clean but the sweep arm will clear any incidental dust away from the stylus. You will however contaminate the record sleeves with the small amount of dust that falls on the record during play which is way less than what you would have with a charged record which pulls dust in like a magnet. Take an old record and rub it with your hands to create a good charge. Now hold the record up to the light in such a way that you can see dust. Dust from over a foot away will swing toward the record and fly right into it. Now think about 10,000 PSI running over it (20,000 total, 10,000 per contact patch) It is no wonder records get noisy, scratchy and dirty with recurrent play. My oldest records, the ones I had when I was 6 years old are painful to listen to even after cleaning and with a modern stylus. My father's records are not much better. He used an old ESL tonearm with an Empire Cartridge and no anti skate. Who knew? 
Anyway, with a large collection none of us play the same record over and over so our records can last forever if taken care of. 
The conductive sweep arm mentioned above is a whopping 20 bucks.
If you get one and want to know a few tricks in set up just message me.

Daveyf, many preferences are a result of mythology which is admittedly hard to combat. If you don't mind dust on your records, don't use a dust cover. I got rid of all my Linns a long time ago because they are irreparably defective. 
Lewm, in order to transfer electrons from your hand to the record there has to be intimate contact. You have to rub your hand firmly back and forth across the record, a maneuver I can see you doing on a regular basis. Remember rubbing your feet on the carpet so you could shock your brother? Don't use the sweep arm. Destroy your records. Why should I care. 

I wish I’d had a brother.
But I do have a nice dust free sister.
if your body is charged all you have to do is touch the LP. The LP is like your unsuspecting brother. You don’t even pay attention to your own analogies.

By the way, you're not the only one who does this, Mijo, but this concept of taking the contact patch area of a stylus tip and typical VTF and from that extrapolating to the pressure in PSI is a specious way to think about the stress on the vinyl, in my opinion.  Why not extrapolate to the surface area of the LP, instead of to a square-inch?  In which case, there is about a million pounds of pressure per LP surface area (estimating that the surface area of a 12-inch LP is about 100 square inches and assuming your own estimate of 10,000 PSI is correct).  Wonder what that would do to record wear.

@mijostyn  "I got rid of all of my Linns a long time ago because they are irreparably defective"

Your post is timely, because I was talking to my Linn dealer yesterday and he related an interesting story. On one of the other forums, there was a chap who was telling everyone that the Linn LP12 was way past its prime, it was always falling out of tune, and was impossible to not only work on but was easily bested in SQ by any new turntable today. My dealer was curious about this guy and so after some back and forth PM’s with him, it was discovered that the poster had last owned a Linn LP12 in 1979, had always set up the table himself and had on occasion swapped out arms, to include a SME 309 and also a arm which he couldn’t remember, but it was heavy and worked well on his later tables. Lastly, the fellow told my dealer that he had heard the Linn recently, which to him was back in 2000! Nonetheless, this chap was 100% sure that his new Technics direct drive from 1980 was easily better than his 1979 Linn. After all, the darned screws were loctighted on the Linn and he couldn’t ever get them loose when he was taking his table apart…

I have NEVER heard of a Linn that was "irreparably defective" only an owner who had no clue how to set it up and refused to allow a qualified Linn dealer to work on it....were you one of those folks??--:0)