Check if an image download from the Internet has already started
Just a note:

... and return type

class CheckingResult {
    public boolean isDownloadingNecessary;
}


Please don't. An encapsulated boolean goes really too far. Especially on Android as an empty class costs 500 bytes. The method is probably fine, the name could be improved to something less boolean-like. You could also use a ConcurrentSet like 

private final Set&lt;imageView&gt; startedDownloads = Sets.newConcurrentHashSet();

private boolean registerDownload(View imageView, String url) {
    return startedDownloads.add(imageView);
}


This assumes Guava, but without it, you could use a ConcurrentHashMap with a dummy value instead. No idea what everything your LOCK_CHECKING_TAG_AND_URL gets used for, so my replacement may not be equivalent. I also removed your tagging in favor of placing the View itself in the set, which may be completely wrong. But why did you chose to use tags instead?

With whatever reason, this should be explained.

If it was because of memory, you could use a WeakReference&lt;View&gt; (with a delegating equals, which makes it too complicated).