Battlerage Vigor, Tempest Style, and Arena Training are all choices for the Weaponmaster Fighter's fighter talent. They cannot be chosen by the Essentials fighter sub-classes (Slayer & Knight).
From the Compendium:
Fighter Talents: Choose one of the following fighter talents
- Arena Training: ...
- Battlerager Vigor: ...
- Brawler Style: ...
- One-Handed Weapon Talent: ...
- Tempest Style: ...
- Two-Handed Weapon Technique: ...
Fighter Talent: You gain a +1 bonus to the attack rolls of weapon attacks.
Weapon Talent: You gain a +1 bonus to the attack rolls of weapon attacks.
The Compendium is up-to-date with all errata (for this content, at any rate). Weaponmaster says "pick one of these". Slayer & Knight say "you get +1 attack"; not "you get +1 attack or you can pick one of the Weaponmaster's talents", just "you get +1 attack".
The Story Behind It All
Mike Mearls is brought in to take over 4e. He doesn't like some of the design choices 4e made (notably the AEDU power scheme for nearly all classes); you can tell he doesn't like it because look how excited he is about all the things he's jettisoning from 4e in making D&D Next. What he wants to do is 4.5, reboot things to work the way he wants them to, but WotC/Hasbro tells him that after all the flak they took for 3.5 another half edition is not even remotely an option, that he absolutely must maintain backwards compatibility with all 4e content already published.
Enter Essentials. Mike Mearls creates the original classes as he envisions them, names them after the class they are, and tacks an extra name onto both his new Essentials classes and the original classes to distinguish them: his two fighters become the Fighter (Slayer) and Fighter (Knight), while the original fighter becomes the Fighter (Weaponmaster). The result is two new classes that have their own class features that work the way he wants them to, but are backwards compatible in that they have access to all previously published feats (and powers, if players of Essentials classes can acquire them) for fighters, even though "Fighter" is no longer a thing.
What This Means
Despite appearances, there is no fighter class in 4e. There are 3 classes, Weaponmaster, Slayer, and Knight, that share a power source (martial) that gives them access to certain things and also share another feature, confusingly called class (fighter) rather than something like archetype, that gives them access to certain things. But 4e doesn't have a fighter class. You can't make "a fighter". You can only make a "slayer with access to fighter resources", a "knight with access to fighter resources", or a "weaponmaster with access to fighter resources". If that seems confusing to you (and judging by the number of questions we get on variants of this topic, it appears to confuse a lot of people) then blame Mike Mearls.
What makes you think Slayers and Knights should have access to Battlerager Vigor, Tempest Style, etc? The fact that they also have "Fighter" in their class names? That means absolutely nothing when talking about class features.